- FindStat

Identifier

St000707: Integer partitions ⟶ ℤ

Values

[2] => 2

[1,1] => 1

[3] => 6

[2,1] => 2

[1,1,1] => 1

[4] => 24

[3,1] => 6

[2,2] => 4

[2,1,1] => 2

[1,1,1,1] => 1

[5] => 120

[4,1] => 24

[3,2] => 12

[3,1,1] => 6

[2,2,1] => 4

[2,1,1,1] => 2

[1,1,1,1,1] => 1

[6] => 720

[5,1] => 120

[4,2] => 48

[4,1,1] => 24

[3,3] => 36

[3,2,1] => 12

[3,1,1,1] => 6

[2,2,2] => 8

[2,2,1,1] => 4

[2,1,1,1,1] => 2

[1,1,1,1,1,1] => 1

[7] => 5040

[6,1] => 720

[5,2] => 240

[5,1,1] => 120

[4,3] => 144

[4,2,1] => 48

[4,1,1,1] => 24

[3,3,1] => 36

[3,2,2] => 24

[3,2,1,1] => 12

[3,1,1,1,1] => 6

[2,2,2,1] => 8

[2,2,1,1,1] => 4

[2,1,1,1,1,1] => 2

[1,1,1,1,1,1,1] => 1

[8] => 40320

[7,1] => 5040

[6,2] => 1440

[6,1,1] => 720

[5,3] => 720

[5,2,1] => 240

[5,1,1,1] => 120

[4,4] => 576

[4,3,1] => 144

[4,2,2] => 96

[4,2,1,1] => 48

[4,1,1,1,1] => 24

[3,3,2] => 72

[3,3,1,1] => 36

[3,2,2,1] => 24

[3,2,1,1,1] => 12

[3,1,1,1,1,1] => 6

[2,2,2,2] => 16

[2,2,2,1,1] => 8

[2,2,1,1,1,1] => 4

[2,1,1,1,1,1,1] => 2

[1,1,1,1,1,1,1,1] => 1

[9] => 362880

[8,1] => 40320

[7,2] => 10080

[7,1,1] => 5040

[6,3] => 4320

[6,2,1] => 1440

[6,1,1,1] => 720

[5,4] => 2880

[5,3,1] => 720

[5,2,2] => 480

[5,2,1,1] => 240

[5,1,1,1,1] => 120

[4,4,1] => 576

[4,3,2] => 288

[4,3,1,1] => 144

[4,2,2,1] => 96

[4,2,1,1,1] => 48

[4,1,1,1,1,1] => 24

[3,3,3] => 216

[3,3,2,1] => 72

[3,3,1,1,1] => 36

[3,2,2,2] => 48

[3,2,2,1,1] => 24

[3,2,1,1,1,1] => 12

[3,1,1,1,1,1,1] => 6

[2,2,2,2,1] => 16

[2,2,2,1,1,1] => 8

[2,2,1,1,1,1,1] => 4

[2,1,1,1,1,1,1,1] => 2

[1,1,1,1,1,1,1,1,1] => 1

[10] => 3628800

[9,1] => 362880

[8,2] => 80640

[8,1,1] => 40320

[7,3] => 30240

[7,2,1] => 10080

>>> Load all 270 entries. <<<

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$F_{2} = q + q^{2}$

$F_{3} = q + q^{2} + q^{6}$

$F_{4} = q + q^{2} + q^{4} + q^{6} + q^{24}$

$F_{5} = q + q^{2} + q^{4} + q^{6} + q^{12} + q^{24} + q^{120}$

$F_{6} = q + q^{2} + q^{4} + q^{6} + q^{8} + q^{12} + q^{24} + q^{36} + q^{48} + q^{120} + q^{720}$

$F_{7} = q + q^{2} + q^{4} + q^{6} + q^{8} + q^{12} + 2\ q^{24} + q^{36} + q^{48} + q^{120} + q^{144} + q^{240} + q^{720} + q^{5040}$

$F_{8} = q + q^{2} + q^{4} + q^{6} + q^{8} + q^{12} + q^{16} + 2\ q^{24} + q^{36} + q^{48} + q^{72} + q^{96} + q^{120} + q^{144} + q^{240} + q^{576} + 2\ q^{720} + q^{1440} + q^{5040} + q^{40320}$

$F_{9} = q + q^{2} + q^{4} + q^{6} + q^{8} + q^{12} + q^{16} + 2\ q^{24} + q^{36} + 2\ q^{48} + q^{72} + q^{96} + q^{120} + q^{144} + q^{216} + q^{240} + q^{288} + q^{480} + q^{576} + 2\ q^{720} + q^{1440} + q^{2880} + q^{4320} + q^{5040} + q^{10080} + q^{40320} + q^{362880}$

$F_{10} = q + q^{2} + q^{4} + q^{6} + q^{8} + q^{12} + q^{16} + 2\ q^{24} + q^{32} + q^{36} + 2\ q^{48} + q^{72} + q^{96} + q^{120} + 2\ q^{144} + q^{192} + q^{216} + q^{240} + q^{288} + q^{480} + q^{576} + 2\ q^{720} + q^{864} + q^{1152} + 2\ q^{1440} + 2\ q^{2880} + q^{4320} + q^{5040} + q^{10080} + q^{14400} + q^{17280} + q^{30240} + q^{40320} + q^{80640} + q^{362880} + q^{3628800}$

$F_{11} = q + q^{2} + q^{4} + q^{6} + q^{8} + q^{12} + q^{16} + 2\ q^{24} + q^{32} + q^{36} + 2\ q^{48} + q^{72} + 2\ q^{96} + q^{120} + 2\ q^{144} + q^{192} + q^{216} + q^{240} + q^{288} + q^{432} + q^{480} + 2\ q^{576} + 2\ q^{720} + q^{864} + q^{960} + q^{1152} + 2\ q^{1440} + 2\ q^{2880} + q^{3456} + 2\ q^{4320} + q^{5040} + q^{5760} + q^{8640} + q^{10080} + q^{14400} + q^{17280} + q^{20160} + q^{30240} + q^{40320} + q^{80640} + q^{86400} + q^{120960} + q^{241920} + q^{362880} + q^{725760} + q^{3628800} + q^{39916800}$

$F_{12} = q + q^{2} + q^{4} + q^{6} + q^{8} + q^{12} + q^{16} + 2\ q^{24} + q^{32} + q^{36} + 2\ q^{48} + q^{64} + q^{72} + 2\ q^{96} + q^{120} + 2\ q^{144} + q^{192} + q^{216} + q^{240} + 2\ q^{288} + q^{384} + q^{432} + q^{480} + 2\ q^{576} + 2\ q^{720} + q^{864} + q^{960} + q^{1152} + q^{1296} + 2\ q^{1440} + q^{1728} + q^{2304} + 3\ q^{2880} + q^{3456} + 2\ q^{4320} + q^{5040} + 2\ q^{5760} + q^{8640} + q^{10080} + q^{13824} + q^{14400} + 2\ q^{17280} + q^{20160} + q^{25920} + q^{28800} + q^{30240} + q^{34560} + q^{40320} + q^{60480} + q^{80640} + q^{86400} + q^{120960} + q^{161280} + q^{241920} + q^{362880} + q^{518400} + q^{604800} + q^{725760} + q^{967680} + q^{2177280} + q^{3628800} + q^{7257600} + q^{39916800} + q^{479001600}$

Description

The product of the factorials of the parts.

Code

def statistic(la):
    return prod(factorial(p) for p in la)

Created

Mar 07, 2017 at 09:36 by Martin Rubey

Updated

Mar 07, 2017 at 09:36 by Martin Rubey