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A271765 Number of set partitions of [n] with minimal block length multiplicity equal to five.

%I A271765 #8 May 15 2018 06:41:34
%S A271765 1,0,0,0,0,945,0,0,0,0,4239235,7567560,82702620,41351310,1658646990,
%T A271765 24448068645,117626817945,239611442070,8260908743395,1834189492520,
%U A271765 4508736346382576,2979073800027325,256635727575051825,2371542394294648575,16374593589666387075
%N A271765 Number of set partitions of [n] with minimal block length multiplicity equal to five.
%H A271765 Alois P. Heinz, <a href="/A271765/b271765.txt">Table of n, a(n) for n = 5..577</a>
%H A271765 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%F A271765 a(n) = A271424(n,5).
%p A271765 with(combinat):
%p A271765 b:= proc(n, i, k) option remember; `if`(n=0, 1,
%p A271765       `if`(i<1, 0, add(multinomial(n, n-i*j, i$j)
%p A271765         *b(n-i*j, i-1, k)/j!, j={0, $k..n/i})))
%p A271765     end:
%p A271765 a:= n-> b(n$2, 5)-b(n$2, 6):
%p A271765 seq(a(n), n=5..30);
%t A271765 multinomial[n_, k_List] := n!/Times @@ (k!);
%t A271765 b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i < 1, 0, Sum[multinomial[n, Join[{n - i*j}, Table[i, j]]]*b[n - i*j, i - 1, k]/j!, {j, Join[{0}, Range[k, n/i]]}]]];
%t A271765 a[n_] := b[n, n, 5] - b[n, n, 6];
%t A271765 Table[a[n], {n, 5, 30}] (* _Jean-François Alcover_, May 15 2018, after _Alois P. Heinz_ *)
%Y A271765 Column k=5 of A271424.
%K A271765 nonn
%O A271765 5,6
%A A271765 _Alois P. Heinz_, Apr 13 2016