A394208 - OEIS

%I #8 Mar 13 2026 10:26:09

%S 1,2,2,2,2,2,2,2,4,6,6,6,6,6,6,6,8,10,10,10,10,12,14,14,16,18,18,18,

%T 18,22,26,26,28,30,30,30,30,34,38,38,42,46,48,50,50,54,58,58,64,70,74,

%U 78,78,82,86,86,92,98,102,106,106,114,122,124,132,140,146,150

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

%C Convolution of A279281 and A279041.

%H Vaclav Kotesovec, <a href="/A394208/b394208.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) ~ Gamma(1 + b/d) * ((4-sqrt(2))*zeta(3/2))^(2/3 + b/(3*d)) * d^(1/6 + b/(3*d)) * exp(3*Pi^(1/3) * ((4-sqrt(2))*zeta(3/2))^(2/3) * (n/d)^(1/3) / 4) / (2^(7/2 + 3*b/(2*d)) * sqrt(3) * Pi^(7/6 - b/(6*d)) * n^(7/6 + b/(3*d))), where d = 3, b = -2.

%t nmax = 120; CoefficientList[Series[Product[(1 + x^(k*(3*k-2))) / (1 - x^(k*(3*k-2))), {k, 1, Floor[Sqrt[1 + 3*nmax]/3 + 1]}], {x, 0, nmax}], x]

%Y Cf. A103265, A279281, A279041.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Mar 12 2026