A376852 - OEIS

%I #9 Oct 08 2024 05:20:00

%S 1,0,1,4,8,12,17,24,36,56,88,136,205,300,428,600,828,1132,1540,2084,

%T 2813,3788,5080,6788,9032,11952,15736,20612,26852,34812,44929,57732,

%U 73900,94268,119852,151932,192072,242172,304584,382164,478364,597400,744365,925384

%N G.f.: Sum_{k>=0} x^(k*(k+1)) * Product_{j=1..k} ((1 + x^j)/(1 - x^j))^2.

%H Vaclav Kotesovec, <a href="/A376852/b376852.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) ~ exp(Pi*sqrt(n)) / (2^(9/2) * n).

%t nmax = 60; CoefficientList[Series[Sum[x^(k*(k+1)) * Product[(1+x^j)/(1-x^j), {j, 1, k}]^2, {k, 0, Sqrt[nmax]}], {x, 0, nmax}], x]

%Y Cf. A333374, A064428, A376813, A376853, A376854.

%K nonn

%O 0,4

%A _Vaclav Kotesovec_, Oct 06 2024