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A133118
Number of partitions of n-set with 3 block sizes.
2
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
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
Column k=3 of A208437.
Sequence in context: A063497 A096363 A033591 * A211336 A092478 A228889
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Sep 18 2007
EXTENSIONS
More terms from Max Alekseyev, Jun 17 2011
STATUS
approved