A394204 - OEIS

%I #8 Mar 13 2026 10:26:22

%S 1,2,2,2,2,2,4,6,6,6,6,6,8,10,10,12,14,14,16,18,18,22,26,26,28,30,30,

%T 34,40,42,46,50,50,54,62,66,72,78,78,82,90,94,100,110,114,122,134,138,

%U 144,158,166,178,194,198,204,218,228,242,262,270,282,302,314,330

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

%C Convolution of A279279 and A278949.

%H Vaclav Kotesovec, <a href="/A394204/b394204.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 = 2, b = -1.

%t nmax = 100; CoefficientList[Series[Product[(1 + x^(k*(2*k-1))) / (1 - x^(k*(2*k-1))), {k, 1, Floor[Sqrt[1 + 8*nmax]/4 + 1]}], {x, 0, nmax}], x]

%Y Cf. A103265, A279279, A278949, A394202, A394203.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Mar 12 2026