A369573 Expansion of Product_{k>=1} (1 + x^(k^2)) / (1 - x^(k^3)).

1, 2, 2, 2, 3, 4, 4, 4, 5, 7, 8, 8, 9, 11, 12, 12, 14, 17, 18, 18, 20, 23, 24, 24, 26, 31, 34, 35, 38, 43, 46, 47, 50, 55, 59, 61, 66, 73, 77, 79, 84, 92, 97, 100, 106, 115, 121, 124, 130, 140, 148, 152, 161, 174, 183, 188, 197, 210, 220, 226, 235, 251, 264, 272

Offset: 0

Author

Vaclav Kotesovec, Jan 26 2024

Keywords

• nonn

Comments

Convolution of A033461 and A003108.

a(n) is the number of pairs (Q(k), P(n-k)), 0<=k<=n, where Q(k) is a partition of k into distinct squares and P(n-k) is a partition of n-k into cubes.

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A003108, A033461, A280204, A280277.

Programs

Mathematica

nmax = 100; CoefficientList[Series[Product[(1+x^(k^2))/(1-x^(k^3)), {k, 1, nmax^(1/2)}], {x, 0, nmax}], x]