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%I #18 Jun 11 2023 11:15:11
%S 1,0,3,8,21,48,126,288,693,1568,3570,7896,17417,37632,80823,171192,
%T 359733,747936,1543192,3155760,6407037,12909024,25835649,51359136,
%U 101470854,199264128,389096028,755591256,1459643343,2805471984,5366161740,10216161336,19362398580
%N Number of partitions of n where there are k^2-1 kinds of parts k.
%F G.f.: 1/Product_{k>=1} (1-x^k)^(k^2-1).
%F a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} A092348(k) * a(n-k).
%o (PARI) my(N=40, x='x+O('x^N)); Vec(1/prod(k=1, N, (1-x^k)^(k^2-1)))
%Y Cf. A023871, A092348, A253289, A363602.
%K nonn,easy
%O 0,3
%A _Seiichi Manyama_, Jun 10 2023
%E Name suggested by _Joerg Arndt_, Jun 11 2023
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