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A275428 Number of set partitions of [n] such that ten is a multiple of each block size.

%I A275428 #8 May 17 2018 03:11:47
%S A275428 1,1,2,4,10,27,82,274,988,3880,16175,72205,340660,1697060,8906990,
%T A275428 48911059,281486144,1687198848,10535484376,68349098640,459596780618,
%U A275428 3202506672898,23052054364956,171418420964352,1314125642973640,10375794542251692,84315714183790792
%N A275428 Number of set partitions of [n] such that ten is a multiple of each block size.
%H A275428 Alois P. Heinz, <a href="/A275428/b275428.txt">Table of n, a(n) for n = 0..607</a>
%H A275428 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%F A275428 E.g.f.: exp(x+x^2/2+x^5/5!+x^10/10!).
%p A275428 a:= proc(n) option remember; `if`(n=0, 1, add(
%p A275428       `if`(j>n, 0, a(n-j)*binomial(n-1, j-1)), j=[1, 2, 5, 10]))
%p A275428     end:
%p A275428 seq(a(n), n=0..30);
%t A275428 a[n_] := a[n] = If[n == 0, 1, Sum[If[j > n, 0, a[n-j]*Binomial[n-1, j-1]], {j, {1, 2, 5, 10}}]];
%t A275428 Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, May 17 2018, translated from Maple *)
%Y A275428 Column k=10 of A275422.
%K A275428 nonn
%O A275428 0,3
%A A275428 _Alois P. Heinz_, Jul 27 2016