login
Expansion of Product_{k>=1} (1 + x^k) * (1 + x^(2*k)) * (1 + x^(3*k)) * (1 + x^(4*k)) / ((1 - x^k) * (1 - x^(2*k)) * (1 - x^(3*k)) * (1 - x^(4*k))).
3

%I #8 Aug 19 2019 04:10:00

%S 1,2,6,14,32,64,132,248,466,838,1488,2560,4370,7272,11988,19424,31160,

%T 49280,77294,119780,184164,280408,423808,635136,945628,1397398,

%U 2052536,2995210,4346416,6270272,8999668,12848584,18257122,25817760,36349600,50952064,71131448

%N Expansion of Product_{k>=1} (1 + x^k) * (1 + x^(2*k)) * (1 + x^(3*k)) * (1 + x^(4*k)) / ((1 - x^k) * (1 - x^(2*k)) * (1 - x^(3*k)) * (1 - x^(4*k))).

%C Convolution of A327046 and A327043.

%H Vaclav Kotesovec, <a href="/A327049/b327049.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) ~ 5^(5/2) * exp(5*Pi*sqrt(n/3)/2) / (2^(17/2)*3^(3/4)*n^(7/4)).

%t nmax = 50; CoefficientList[Series[Product[(1+x^k) * (1+x^(2*k)) * (1+x^(3*k)) * (1+x^(4*k))/((1-x^k) * (1-x^(2*k)) * (1-x^(3*k)) * (1-x^(4*k))), {k, 1, nmax}], {x, 0, nmax}], x]

%Y Cf. A015128, A246584, A327048, A327050.

%Y Cf. A301554.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Aug 16 2019