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A275424 Number of set partitions of [n] such that six is a multiple of each block size.

%I A275424 #8 May 17 2018 03:11:20
%S A275424 1,1,2,5,14,46,167,659,2836,13064,64076,333928,1834438,10592518,
%T A275424 64136528,405519766,2672202304,18315499424,130245129112,959527765480,
%U A275424 7311915167696,57536223460640,466963917417152,3904133599120624,33583586584746728,296948602314737576
%N A275424 Number of set partitions of [n] such that six is a multiple of each block size.
%H A275424 Alois P. Heinz, <a href="/A275424/b275424.txt">Table of n, a(n) for n = 0..603</a>
%H A275424 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%F A275424 E.g.f.: exp(x+x^2/2+x^3/6+x^6/6!).
%p A275424 a:= proc(n) option remember; `if`(n=0, 1, add(
%p A275424       `if`(j>n, 0, a(n-j)*binomial(n-1, j-1)), j=[1, 2, 3, 6]))
%p A275424     end:
%p A275424 seq(a(n), n=0..30);
%t A275424 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}}]];
%t A275424 Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, May 17 2018, translated from Maple *)
%Y A275424 Column k=6 of A275422.
%K A275424 nonn
%O A275424 0,3
%A A275424 _Alois P. Heinz_, Jul 27 2016