A275097 Number of set partitions of [8*n] such that within each block the numbers of elements from all residue classes modulo 8 are equal.

1, 1, 129, 286498, 4802367617, 386652630390626, 112344305783644570242, 96703375432646667737903621, 213426677887357366350726096998529, 1081530653290057746718498987187644516546, 11534313393388449518393789691807687515711518754

Offset: 0

Author

Alois P. Heinz, Jul 16 2016

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..91
• J.-M. Sixdeniers, K. A. Penson and A. I. Solomon, Extended Bell and Stirling Numbers From Hypergeometric Exponentiation, J. Integer Seqs. Vol. 4 (2001), #01.1.4.

Crossrefs

Column k=8 of A275043.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(
      binomial(n, j)^8*(n-j)*a(j), j=0..n-1)/n)
    end:
seq(a(n), n=0..12);

Formula

Sum_{n>=0} a(n) * x^n / (n!)^8 = exp(Sum_{n>=1} x^n / (n!)^8). - Ilya Gutkovskiy, Jul 17 2020