login
Number of partitions of n where there are k^2+1 kinds of parts k.
2

%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