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Expansion of Product_{k>=1} (1 + x^(k^2)) / (1 - x^(k^3)).
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%I #12 Jan 28 2024 09:01:34

%S 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,

%T 35,38,43,46,47,50,55,59,61,66,73,77,79,84,92,97,100,106,115,121,124,

%U 130,140,148,152,161,174,183,188,197,210,220,226,235,251,264,272

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

%C Convolution of A033461 and A003108.

%C 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.

%H Vaclav Kotesovec, <a href="/A369573/b369573.txt">Table of n, a(n) for n = 0..10000</a>

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

%Y Cf. A003108, A033461, A280204, A280277.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Jan 26 2024