cp's OEIS Frontend

A271766 Number of set partitions of [n] with minimal block length multiplicity equal to six.

%I A271766 #8 May 15 2018 06:41:40
%S A271766 1,0,0,0,0,0,10395,0,0,0,0,0,383563180,523783260,6547290750,
%T A271766 3055402350,157964301495,14054850810,34828180582195,91670862398500,
%U A271766 448593283888750,11612610774464700,7681370284312725,6594450798260325,179804372693675480751,11896760875264765500
%N A271766 Number of set partitions of [n] with minimal block length multiplicity equal to six.
%H A271766 Alois P. Heinz, <a href="/A271766/b271766.txt">Table of n, a(n) for n = 6..577</a>
%H A271766 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%F A271766 a(n) = A271424(n,6).
%p A271766 with(combinat):
%p A271766 b:= proc(n, i, k) option remember; `if`(n=0, 1,
%p A271766       `if`(i<1, 0, add(multinomial(n, n-i*j, i$j)
%p A271766         *b(n-i*j, i-1, k)/j!, j={0, $k..n/i})))
%p A271766     end:
%p A271766 a:= n-> b(n$2, 6)-b(n$2, 7):
%p A271766 seq(a(n), n=6..30);
%t A271766 multinomial[n_, k_List] := n!/Times @@ (k!);
%t A271766 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 A271766 a[n_] := b[n, n, 6] - b[n, n, 7];
%t A271766 Table[a[n], {n, 6, 30}] (* _Jean-François Alcover_, May 15 2018, after _Alois P. Heinz_ *)
%Y A271766 Column k=6 of A271424.
%K A271766 nonn
%O A271766 6,7
%A A271766 _Alois P. Heinz_, Apr 13 2016