|
%I #9 Mar 08 2015 04:19:29
%S 1,3,8,23,55,129,291,627,1317,2697,5398,10589,20421,38743,72452,
%T 133724,243792,439496,784070,1385195,2424971,4209094,7247141,12383496,
%U 21008559,35398548,59259781,98595110,163077878,268221706,438791204,714142139,1156552537
%N G.f.: Product_{k>=1} (1+x^k)^(2*k+1).
%H Vaclav Kotesovec, <a href="/A255834/b255834.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) ~ Zeta(3)^(1/6) * exp(-Pi^4 / (2592*Zeta(3)) + Pi^2 * n^(1/3) / (12*(3*Zeta(3))^(1/3)) + 3^(4/3)/2*Zeta(3)^(1/3) * n^(2/3)) / (2^(7/6)* 3^(1/3) * sqrt(Pi) * n^(2/3)), where Zeta(3) = A002117.
%t nmax=50; CoefficientList[Series[Product[(1+x^k)^(2*k+1),{k,1,nmax}],{x,0,nmax}],x]
%Y Cf. A026007, A120844, A219555, A255835, A255836.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Mar 07 2015
|
