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A275427 Number of set partitions of [n] such that nine is a multiple of each block size.

%I A275427 #8 May 17 2018 03:11:41
%S A275427 1,1,1,2,5,11,31,106,337,1206,5031,20241,86901,421422,2014377,
%T A275427 10015461,54946881,301009311,1692429867,10319449158,63321896601,
%U A275427 395830490301,2648669976261,17920165424382,122976000215289,894420751179276,6596034524038701,49207275464475051
%N A275427 Number of set partitions of [n] such that nine is a multiple of each block size.
%H A275427 Alois P. Heinz, <a href="/A275427/b275427.txt">Table of n, a(n) for n = 0..617</a>
%H A275427 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%F A275427 E.g.f.: exp(x+x^3/6+x^9/9!).
%p A275427 a:= proc(n) option remember; `if`(n=0, 1, add(
%p A275427       `if`(j>n, 0, a(n-j)*binomial(n-1, j-1)), j=[1, 3, 9]))
%p A275427     end:
%p A275427 seq(a(n), n=0..30);
%t A275427 a[n_] := a[n] = If[n == 0, 1, Sum[If[j > n, 0, a[n-j]*Binomial[n-1, j-1]], {j, {1, 3, 9}}]];
%t A275427 Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, May 17 2018, translated from Maple *)
%Y A275427 Column k=9 of A275422.
%K A275427 nonn
%O A275427 0,4
%A A275427 _Alois P. Heinz_, Jul 27 2016