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A271770 Number of set partitions of [n] with minimal block length multiplicity equal to ten.

%I A271770 #8 May 15 2018 06:41:09
%S A271770 1,0,0,0,0,0,0,0,0,0,654729075,0,0,0,0,0,0,0,0,0,1228555090548911125,
%T A271770 55437426478058625,1034831960923761000,375268733082243000,
%U A271770 42378561928787584500,2126522820799377000,2014348742002209863250,10413707343032243250
%N A271770 Number of set partitions of [n] with minimal block length multiplicity equal to ten.
%H A271770 Alois P. Heinz, <a href="/A271770/b271770.txt">Table of n, a(n) for n = 10..578</a>
%H A271770 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%F A271770 a(n) = A271424(n,10).
%p A271770 with(combinat):
%p A271770 b:= proc(n, i, k) option remember; `if`(n=0, 1,
%p A271770       `if`(i<1, 0, add(multinomial(n, n-i*j, i$j)
%p A271770         *b(n-i*j, i-1, k)/j!, j={0, $k..n/i})))
%p A271770     end:
%p A271770 a:= n-> b(n$2, 10)-b(n$2, 11):
%p A271770 seq(a(n), n=10..40);
%t A271770 multinomial[n_, k_List] := n!/Times @@ (k!);
%t A271770 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 A271770 a[n_] := b[n, n, 10] - b[n, n, 11];
%t A271770 Table[a[n], {n, 10, 40}] (* _Jean-François Alcover_, May 15 2018, after _Alois P. Heinz_ *)
%Y A271770 Column k=10 of A271424.
%K A271770 nonn
%O A271770 10,11
%A A271770 _Alois P. Heinz_, Apr 13 2016