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Number of set partitions of [n] such that nine is a multiple of each block size.
2

%I #8 May 17 2018 03:11:41

%S 1,1,1,2,5,11,31,106,337,1206,5031,20241,86901,421422,2014377,

%T 10015461,54946881,301009311,1692429867,10319449158,63321896601,

%U 395830490301,2648669976261,17920165424382,122976000215289,894420751179276,6596034524038701,49207275464475051

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

%H Alois P. Heinz, <a href="/A275427/b275427.txt">Table of n, a(n) for n = 0..617</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>

%F E.g.f.: exp(x+x^3/6+x^9/9!).

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

%p `if`(j>n, 0, a(n-j)*binomial(n-1, j-1)), j=[1, 3, 9]))

%p end:

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

%t 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 Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, May 17 2018, translated from Maple *)

%Y Column k=9 of A275422.

%K nonn

%O 0,4

%A _Alois P. Heinz_, Jul 27 2016