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A275424 Number of set partitions of [n] such that six is a multiple of each block size. 2
1, 1, 2, 5, 14, 46, 167, 659, 2836, 13064, 64076, 333928, 1834438, 10592518, 64136528, 405519766, 2672202304, 18315499424, 130245129112, 959527765480, 7311915167696, 57536223460640, 466963917417152, 3904133599120624, 33583586584746728, 296948602314737576 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..603

Wikipedia, Partition of a set

FORMULA

E.g.f.: exp(x+x^2/2+x^3/6+x^6/6!).

MAPLE

a:= proc(n) option remember; `if`(n=0, 1, add(

      `if`(j>n, 0, a(n-j)*binomial(n-1, j-1)), j=[1, 2, 3, 6]))

    end:

seq(a(n), n=0..30);

MATHEMATICA

a[n_] := a[n] = If[n == 0, 1, Sum[If[j > n, 0, a[n-j]*Binomial[n-1, j-1]], {j, {1, 2, 3, 6}}]];

Table[a[n], {n, 0, 30}] (* Jean-Fran├žois Alcover, May 17 2018, translated from Maple *)

CROSSREFS

Column k=6 of A275422.

Sequence in context: A240616 A240617 A001680 * A328429 A107268 A231211

Adjacent sequences:  A275421 A275422 A275423 * A275425 A275426 A275427

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jul 27 2016

STATUS

approved

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Last modified February 19 22:04 EST 2020. Contains 332060 sequences. (Running on oeis4.)