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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
OFFSET
0,3
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
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 12 2019
STATUS
approved