A133118 Number of partitions of n-set with 3 block sizes.

60, 315, 2268, 14742, 72180, 464640, 2676366, 16400098, 94209206, 673282610, 4095231104, 29371828846, 197547348216, 1513916607683, 10904464442572, 87070803499372, 673555061736062, 5718121102062336, 47028289679340734, 418812093667530755, 3680961843042545490, 34161428275433710485

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];
Array[a, 22, 6] (* Jean-François Alcover, May 24 2019, after Alois P. Heinz in A208437 *)

Crossrefs

Cf. A038041, A088142, A122404, A005225, A005772.

Column k=3 of A208437.

Sequence in context: A063497 A096363 A033591 * A211336 A092478 A228889

Adjacent sequences: A133115 A133116 A133117 * A133119 A133120 A133121

Keyword

easy,nonn

Author

Vladeta Jovovic, Sep 18 2007

Extensions

More terms from Max Alekseyev, Jun 17 2011

Status

approved