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A323295 Number of ways to fill a matrix with the first n positive integers. 12
1, 1, 4, 12, 72, 240, 2880, 10080, 161280, 1088640, 14515200, 79833600, 2874009600, 12454041600, 348713164800, 5230697472000, 104613949440000, 711374856192000, 38414242234368000, 243290200817664000, 14597412049059840000, 204363768686837760000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..21.

FORMULA

a(n) = A000005(n) * n! for n > 0, a(0) = 1.

E.g.f.: 1 + Sum_{k>=1} x^k/(1 - x^k). - Ilya Gutkovskiy, Sep 13 2019

EXAMPLE

The a(4) = 72 matrices consist of:

  24 row/column permutations of [1 2 3 4]

+

  4 row/column permutations of [1 2]

                               [3 4]

+

  4 row/column permutations of [1 2]

                               [4 3]

+

  4 row/column permutations of [1 3]

                               [2 4]

+

  4 row/column permutations of [1 3]

                               [4 2]

+

  4 row/column permutations of [1 4]

                               [2 3]

+

  4 row/column permutations of [1 4]

                               [3 2]

+

  24 row/column permutations of [1]

                                [2]

                                [3]

                                [4]

MATHEMATICA

Join[{1}, Table[DivisorSigma[0, n]*n!, {n, 30}]]

PROG

(PARI) a(n) = if (n==0, 1, numdiv(n)*n!); \\ Michel Marcus, Jan 15 2019

CROSSREFS

Cf. A000005, A000142, A038041, A053529, A057625, A061095, A120733, A121860.

Cf. A323300, A323301, A323307, A323351.

Sequence in context: A009621 A335907 A013195 * A166746 A052558 A190340

Adjacent sequences:  A323292 A323293 A323294 * A323296 A323297 A323298

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jan 12 2019

STATUS

approved

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Last modified April 15 10:49 EDT 2021. Contains 342977 sequences. (Running on oeis4.)