A377077 - OEIS

%I #8 Oct 15 2024 05:11:40

%S 0,0,0,0,0,0,0,1,1,2,3,5,7,11,14,20,26,35,44,58,71,90,110,136,163,199,

%T 235,282,332,392,456,535,617,716,822,946,1079,1236,1402,1596,1806,

%U 2046,2306,2606,2929,3299,3704,4163,4667,5241,5870,6585,7378,8273,9268,10397

%N G.f.: Sum_{k>=0} x^(7*k^2) / Product_{j=1..7*k-1} (1 - x^j).

%H Vaclav Kotesovec, <a href="/A377077/b377077.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) ~ r^2 * (7*log(r)^2 + polylog(2, r^2))^(1/4) * exp(2*sqrt((7*log(r)^2 + polylog(2, r^2))*n)) / (2*sqrt(7*Pi*(7 - 5*r^2)) * n^(3/4)), where r = 0.839833147032421662... is the positive real root of the equation r^2 = 1 - r^7.

%t nmax = 100; CoefficientList[Series[Sum[x^(7*k^2)/Product[1-x^j, {j, 1, 7*k-1}], {k, 1, Sqrt[nmax/7]}], {x, 0, nmax}], x]

%Y Column 7 of A350889.

%K nonn

%O 0,10

%A _Vaclav Kotesovec_, Oct 15 2024