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G.f.: Product_{k>=1} (1 + x^k) / (1 - x^(k^2)).
5

%I #8 Jan 28 2024 08:58:57

%S 1,2,3,5,8,12,17,24,33,46,62,82,108,141,182,233,297,375,472,590,733,

%T 907,1117,1369,1671,2034,2465,2978,3586,4304,5152,6149,7319,8689,

%U 10293,12162,14340,16871,19806,23207,27139,31678,36909,42932,49851,57794,66897

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

%C Convolution of A000009 and A001156.

%H Vaclav Kotesovec, <a href="/A280276/b280276.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) ~ exp(Pi*sqrt(n/3) + 3^(1/4) * Zeta(3/2) * n^(1/4) / sqrt(2) - 3*Zeta(3/2)^2 / (16*Pi)) / (8*sqrt(6*Pi)*n).

%t nmax=80; CoefficientList[Series[Product[(1+x^k)/(1-x^(k^2)), {k, 1, nmax}], {x, 0, nmax}], x]

%Y Cf. A000009, A001156, A087154, A103265, A280277, A369570, A369574.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Dec 30 2016