OFFSET
6,1
LINKS
Alois P. Heinz, Table of n, a(n) for n = 6..300
FORMULA
We obtain e.g.f. for number of partitions of n-set with m block sizes if we substitute x(i) with -Sum_{k>0} (1-exp(x^k/k!))^i in cycle index Z(S(m); x(1),x(2),...,x(n)) of symmetric group S(m) of degree m.
MATHEMATICA
multinomial[n_, k_List] := n!/Times @@ (k!);
b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, Sum[multinomial[n, Prepend[Table[i, {j}], n - i*j]]/j!*b[n - i*j, i - 1]*If[j == 0, 1, x], {j, 0, n/i}]]];
a[n_] := Coefficient[b[n, n], x, 3];
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Sep 18 2007
EXTENSIONS
More terms from Max Alekseyev, Jun 17 2011
STATUS
approved