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A363601
Number of partitions of n where there are k^2-1 kinds of parts k.
2
1, 0, 3, 8, 21, 48, 126, 288, 693, 1568, 3570, 7896, 17417, 37632, 80823, 171192, 359733, 747936, 1543192, 3155760, 6407037, 12909024, 25835649, 51359136, 101470854, 199264128, 389096028, 755591256, 1459643343, 2805471984, 5366161740, 10216161336, 19362398580
OFFSET
0,3
FORMULA
G.f.: 1/Product_{k>=1} (1-x^k)^(k^2-1).
a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} A092348(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