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A275099
Number of set partitions of [10*n] such that within each block the numbers of elements from all residue classes modulo 10 are equal.
2
1, 1, 513, 10136746, 2672797504001, 5260857687009765626, 53531132944198868710856802, 2185249026716732313958375321948613, 297263694975439941710846391262298377605633, 116941828532092016226313310933885429108622288425362
OFFSET
0,3
LINKS
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.
FORMULA
Sum_{n>=0} a(n) * x^n / (n!)^10 = exp(Sum_{n>=1} x^n / (n!)^10). - Ilya Gutkovskiy, Jul 17 2020
MAPLE
a:= proc(n) option remember; `if`(n=0, 1, add(
binomial(n, j)^10*(n-j)*a(j), j=0..n-1)/n)
end:
seq(a(n), n=0..12);
MATHEMATICA
a[n_] := a[n] = If[n==0, 1, Sum[Binomial[n, j]^10*(n-j)*a[j], {j, 0, n-1}]/n];
Table[a[n], {n, 0, 12}] (* Jean-François Alcover, Jun 27 2022, after Alois P. Heinz *)
CROSSREFS
Column k=10 of A275043.
Sequence in context: A283369 A103351 A291507 * A238615 A213065 A045054
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 16 2016
STATUS
approved