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A271764 Number of set partitions of [n] with minimal block length multiplicity equal to four.

%I A271764 #8 May 15 2018 06:41:28
%S A271764 1,0,0,0,105,0,0,0,67375,135135,1261260,675675,50925875,97847750,
%T A271764 703993290,6215737710,228687298476,58017429575,11262925616250,
%U A271764 72813288304295,2841531210935725,11311740884766630,252469888906590355,2207276997956560530,28579415631325499655
%N A271764 Number of set partitions of [n] with minimal block length multiplicity equal to four.
%H A271764 Alois P. Heinz, <a href="/A271764/b271764.txt">Table of n, a(n) for n = 4..577</a>
%H A271764 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%F A271764 a(n) = A271424(n,4).
%p A271764 with(combinat):
%p A271764 b:= proc(n, i, k) option remember; `if`(n=0, 1,
%p A271764       `if`(i<1, 0, add(multinomial(n, n-i*j, i$j)
%p A271764         *b(n-i*j, i-1, k)/j!, j={0, $k..n/i})))
%p A271764     end:
%p A271764 a:= n-> b(n$2, 4)-b(n$2, 5):
%p A271764 seq(a(n), n=4..30);
%t A271764 multinomial[n_, k_List] := n!/Times @@ (k!);
%t A271764 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 A271764 a[n_] := b[n, n, 4] - b[n, n, 5];
%t A271764 Table[a[n], {n, 4, 30}] (* _Jean-François Alcover_, May 15 2018, after _Alois P. Heinz_ *)
%Y A271764 Column k=4 of A271424.
%K A271764 nonn
%O A271764 4,5
%A A271764 _Alois P. Heinz_, Apr 13 2016