A271767 - OEIS

%I #8 May 15 2018 06:41:46

%S 1,0,0,0,0,0,0,135135,0,0,0,0,0,0,51925673800,43212118950,

%T 607370338575,265034329560,17166996346500,1305093289500,

%U 584129638842750,56071685084790375,176898040019801100,518112685551586125,26529011711988035250,4672320885518286000

%N Number of set partitions of [n] with minimal block length multiplicity equal to seven.

%H Alois P. Heinz, <a href="/A271767/b271767.txt">Table of n, a(n) for n = 7..577</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>

%F a(n) = A271424(n,7):

%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, 7)-b(n$2, 8):

%p seq(a(n), n=7..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, 7] - b[n, n, 8];

%t Table[a[n], {n, 7, 35}] (* _Jean-François Alcover_, May 15 2018, after _Alois P. Heinz_ *)

%Y Column k=7 of A271424.

%K nonn

%O 7,8

%A _Alois P. Heinz_, Apr 13 2016