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A271769 Number of set partitions of [n] with minimal block length multiplicity equal to nine.

%I A271769 #8 May 15 2018 06:41:57
%S A271769 1,0,0,0,0,0,0,0,0,34459425,0,0,0,0,0,0,0,0,3139051466175625,
%T A271769 452214824811750,7749317679728625,2980506799895625,284294494759275000,
%U A271769 16245399700530000,12231973704514063500,75947243599977750,558368602431954063750,668351312267239068593125
%N A271769 Number of set partitions of [n] with minimal block length multiplicity equal to nine.
%H A271769 Alois P. Heinz, <a href="/A271769/b271769.txt">Table of n, a(n) for n = 9..578</a>
%H A271769 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%F A271769 a(n) = A271424(n,9).
%p A271769 with(combinat):
%p A271769 b:= proc(n, i, k) option remember; `if`(n=0, 1,
%p A271769       `if`(i<1, 0, add(multinomial(n, n-i*j, i$j)
%p A271769         *b(n-i*j, i-1, k)/j!, j={0, $k..n/i})))
%p A271769     end:
%p A271769 a:= n-> b(n$2, 9)-b(n$2, 10):
%p A271769 seq(a(n), n=9..40);
%t A271769 multinomial[n_, k_List] := n!/Times @@ (k!);
%t A271769 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 A271769 a[n_] := b[n, n, 9] - b[n, n, 10];
%t A271769 Table[a[n], {n, 9, 40}] (* _Jean-François Alcover_, May 15 2018, after _Alois P. Heinz_ *)
%Y A271769 Column k=9 of A271424.
%K A271769 nonn
%O A271769 9,10
%A A271769 _Alois P. Heinz_, Apr 13 2016