The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #6 May 28 2019 17:05:32
%S 1,6,30,204,1014,5716,31212,163480,826278,4320132,22096324,110079016,
%T 552324796,2721379144,13415146648,66143801648,321016593670,
%U 1549027853156,7506317522132,35931754574216,171790455469140,820584857999448,3893605676834920,18400781049682512
%N a(n) = 4^n * [x^n] 1/sqrt(1-x) * Product_{k>=1} (1 + x^k).
%F a(n) ~ exp(Pi*sqrt(n/3)) * 2^(2*n - 3/2) / sqrt(Pi*n).
%F a(n) = Sum_{j=0..n} A325949(j)*4^(n-j).
%t nmax = 30; CoefficientList[Series[1/(1-x)^(1/2) * Product[(1+x^k), {k, 1, nmax}], {x, 0, nmax}], x] * 4^Range[0, nmax]
%Y Cf. A000009, A325947, A325949.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, May 28 2019