%I #13 Jun 11 2023 11:14:55

%S 1,2,6,20,52,140,356,880,2123,5016,11610,26400,59130,130476,284216,

%T 611592,1301344,2740194,5713930,11806144,24184908,49142504,99091244,

%U 198360536,394342884,778818658,1528531702,2982017956,5784365082,11158728448,21413292868

%N Number of partitions of n into distinct parts where there are k^2+1 kinds of part k.

%F G.f.: Product_{k>=1} (1+x^k)^(k^2+1).

%F a(0) = 1; a(n) = (-1/n) * Sum_{k=1..n} ( Sum_{d|k} (-1)^(k/d) * d * (d^2+1) ) * a(n-k).

%o (PARI) my(N=40, x='x+O('x^N)); Vec(prod(k=1, N, (1+x^k)^(k^2+1)))

%Y Cf. A027998, A219555, A255834, A363599.

%Y Cf. A363602.

%K nonn,easy

%O 0,2

%A _Seiichi Manyama_, Jun 10 2023

%E Name suggested by _Joerg Arndt_, Jun 11 2023