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A275426 Number of set partitions of [n] such that eight is a multiple of each block size.

%I A275426 #8 May 17 2018 03:11:33
%S A275426 1,1,2,4,11,31,106,372,1500,6220,28696,136016,702802,3727946,21253324,
%T A275426 124231096,772458366,4918962462,33061094812,227303566648,
%U A275426 1639389311906,12082068225466,92951836390172,729991698024568,5960615982017512,49636995406898376
%N A275426 Number of set partitions of [n] such that eight is a multiple of each block size.
%H A275426 Alois P. Heinz, <a href="/A275426/b275426.txt">Table of n, a(n) for n = 0..604</a>
%H A275426 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%F A275426 E.g.f.: exp(x+x^2/2+x^4/24+x^8/8!).
%p A275426 a:= proc(n) option remember; `if`(n=0, 1, add(
%p A275426       `if`(j>n, 0, a(n-j)*binomial(n-1, j-1)), j=[1, 2, 4, 8]))
%p A275426     end:
%p A275426 seq(a(n), n=0..30);
%t A275426 a[n_] := a[n] = If[n == 0, 1, Sum[If[j > n, 0, a[n-j]*Binomial[n-1, j-1]], {j, {1, 2, 4, 8}}]];
%t A275426 Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, May 17 2018, translated from Maple *)
%Y A275426 Column k=8 of A275422.
%K A275426 nonn
%O A275426 0,3
%A A275426 _Alois P. Heinz_, Jul 27 2016