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
Offset: 0
Programs
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PARI
my(N=40, x='x+O('x^N)); Vec(1/prod(k=1, N, (1-x^k)^(k^2+1)))
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).
Extensions
Name suggested by Joerg Arndt, Jun 11 2023