%I #15 May 24 2019 14:29:56

%S 60,315,2268,14742,72180,464640,2676366,16400098,94209206,673282610,

%T 4095231104,29371828846,197547348216,1513916607683,10904464442572,

%U 87070803499372,673555061736062,5718121102062336,47028289679340734,418812093667530755,3680961843042545490,34161428275433710485

%N Number of partitions of n-set with 3 block sizes.

%H Alois P. Heinz, <a href="/A133118/b133118.txt">Table of n, a(n) for n = 6..300</a>

%F 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.

%t multinomial[n_, k_List] := n!/Times @@ (k!);

%t 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}]]];

%t a[n_] := Coefficient[b[n, n], x, 3];

%t Array[a, 22, 6] (* _Jean-François Alcover_, May 24 2019, after _Alois P. Heinz_ in A208437 *)

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

%Y Column k=3 of A208437.

%K easy,nonn

%O 6,1

%A _Vladeta Jovovic_, Sep 18 2007

%E More terms from _Max Alekseyev_, Jun 17 2011