A363599 - OEIS

A363599

Number of partitions of n into distinct parts where there are k^2-1 kinds of part k.

1, 0, 3, 8, 18, 48, 109, 264, 594, 1360, 2988, 6552, 14115, 30048, 63288, 131800, 271953, 555792, 1126583, 2264472, 4518051, 8948544, 17603781, 34405272, 66828247, 129040704, 247765665, 473160696, 898924929, 1699331808, 3197083220, 5987288352, 11162934948

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..32.

FORMULA

G.f.: Product_{k>=1} (1+x^k)^(k^2-1).

a(0) = 1; a(n) = (-1/n) * Sum_{k=1..n} ( Sum_{d|k} (-1)^(k/d) * d * (d^2-1) ) * a(n-k).

PROG

(PARI) my(N=40, x='x+O('x^N)); Vec(prod(k=1, N, (1+x^k)^(k^2-1)))

CROSSREFS

Cf. A027998, A052812, A255835, A363600.