A332259 a(n) = n! * [x^n] 1 / (1 - Sum_{d|n} x^d / d!).

1, 1, 3, 7, 67, 121, 4551, 5041, 405371, 888721, 65326213, 39916801, 27854708575, 6227020801, 5417436748153, 6968620334677, 2744261072866171, 355687428096001, 2984245819328278077, 121645100408832001, 1177257398964663961517, 545405274481512519361

Offset: 0

Author

Ilya Gutkovskiy, Feb 08 2020

Keywords

• nonn

Comments

Number of ordered set partitions of [n] such that n is a multiple of each block size.

Crossrefs

Cf. A000670, A275429.

Programs

Mathematica

Table[n! SeriesCoefficient[1/(1 - Sum[Boole[Mod[n, k] == 0] x^k/k!, {k, 1, n}]), {x, 0, n}], {n, 0, 22}]

PARI

a(n) = {n! * polcoef(1/(1 - sumdiv(n, d, x^d/d!) + O(x*x^n)), n)} \\ Andrew Howroyd, Feb 08 2020