A363602 - OEIS

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A363602

Number of partitions of n where there are k^2+1 kinds of parts k.

1, 2, 8, 24, 72, 196, 532, 1368, 3467, 8520, 20580, 48664, 113330, 259588, 586692, 1308304, 2883427, 6283192, 13551344, 28940688, 61246052, 128492516, 267388008, 552126648, 1131750735, 2303690862, 4658080756, 9358912416, 18689701580, 37106245300, 73259451208

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..30.

FORMULA

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

a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} A092345(k) * a(n-k).

PROG

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

CROSSREFS

Cf. A023871, A092345, A363601.