A305124 - OEIS

A305124

G.f.: Sum_{k>=1} x^(2*k-1)/(1+x^(2*k-1)) * Product_{k>=1} (1+x^k)/(1-x^k).

%I #6 May 26 2018 13:00:55

%S 0,1,1,4,7,14,24,42,69,113,178,276,420,630,930,1360,1963,2804,3969,

%T 5568,7746,10700,14672,19986,27060,36423,48754,64928,86038,113478,

%U 149012,194842,253737,329172,425452,547952,703343,899858,1147680,1459364,1850310,2339432

%N G.f.: Sum_{k>=1} x^(2*k-1)/(1+x^(2*k-1)) * Product_{k>=1} (1+x^k)/(1-x^k).

%C Convolution of A305123 and A000009.

%H Vaclav Kotesovec, <a href="/A305124/b305124.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = A305101(n) - A305122(n).

%F a(n) ~ exp(sqrt(n)*Pi) * log(2) / (8*Pi*sqrt(n)).

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

%Y Cf. A305102, A305101, A305104, A305122, A305105.

%Y Cf. A116676, A305123.

%K nonn

%O 0,4

%A _Vaclav Kotesovec_, May 26 2018