A301589 - OEIS

%I #8 Dec 29 2021 14:00:25

%S 1,1,3,3,7,9,15,20,31,41,61,79,113,146,201,260,349,447,589,748,972,

%T 1226,1571,1968,2495,3106,3900,4825,6008,7392,9137,11181,13731,16719,

%U 20409,24737,30032,36243,43783,52620,63282,75760,90727,108222,129097,153464

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

%C Euler transform of A010872.

%H Seiichi Manyama, <a href="/A301589/b301589.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) ~ exp(Pi*sqrt(2*n/3)) * Pi^(2/3) / (2^(5/6) * 3^(7/6) * Gamma(1/3) * n^(5/6)).

%t nmax = 60; CoefficientList[Series[Product[1/(1-x^k)^Mod[k, 3], {k, 1, nmax}], {x, 0, nmax}], x]

%Y Cf. A010872, A301588.

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, Mar 24 2018