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%I #8 May 15 2018 06:41:52
%S 1,0,0,0,0,0,0,0,2027025,0,0,0,0,0,0,0,10652498631775,4141161399375,
%T 64602117830250,26428139112375,2096632369581750,137561852302875,
%U 80768458994973750,609202488769875,158980016052580597875,353341814230502847750,1344898884799733513250
%N Number of set partitions of [n] with minimal block length multiplicity equal to eight.
%H Alois P. Heinz, <a href="/A271768/b271768.txt">Table of n, a(n) for n = 8..578</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%F a(n) = A271424(n,8).
%p with(combinat):
%p b:= proc(n, i, k) option remember; `if`(n=0, 1,
%p `if`(i<1, 0, add(multinomial(n, n-i*j, i$j)
%p *b(n-i*j, i-1, k)/j!, j={0, $k..n/i})))
%p end:
%p a:= n-> b(n$2, 8)-b(n$2, 9):
%p seq(a(n), n=8..35);
%t multinomial[n_, k_List] := n!/Times @@ (k!);
%t 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 a[n_] := b[n, n, 8] - b[n, n, 9];
%t Table[a[n], {n, 8, 35}] (* _Jean-François Alcover_, May 15 2018, after _Alois P. Heinz_ *)
%Y Column k=8 of A271424.
%K nonn
%O 8,9
%A _Alois P. Heinz_, Apr 13 2016
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