%I #18 Jun 11 2023 11:15:07
%S 1,2,8,24,72,196,532,1368,3467,8520,20580,48664,113330,259588,586692,
%T 1308304,2883427,6283192,13551344,28940688,61246052,128492516,
%U 267388008,552126648,1131750735,2303690862,4658080756,9358912416,18689701580,37106245300,73259451208
%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} A092345(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, A092345, A363601.
%K nonn,easy
%O 0,2
%A _Seiichi Manyama_, Jun 10 2023
%E Name suggested by _Joerg Arndt_, Jun 11 2023