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URL: https://oeis.org/A363602

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A363602
Number of partitions of n where there are k^2+1 kinds of parts k.
8
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
0,2
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
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Jun 10 2023
EXTENSIONS
Name suggested by Joerg Arndt, Jun 11 2023
STATUS
approved