A377585 - OEIS

%I #5 Nov 02 2024 05:22:47

%S 1,1,7,61,577,7381,96511,1619857,28368481,560654857,12100090231,

%T 282510616741,7098784113697,190647458125021,5461212525476527,

%U 165494332157561401,5306572876379307841,178898083900878623377,6336492991778941139431,234867483921621706900237,9096385945218131126509441

%N E.g.f.: exp(Sum_{k>=1} A057660(k) * x^k).

%H Vaclav Kotesovec, <a href="/A377585/b377585.txt">Table of n, a(n) for n = 0..400</a>

%F a(n) ~ 3^(1/4) * zeta(3)^(1/8) * exp(sqrt(Pi)*n^(1/4)/(6^(3/2)*zeta(3)^(1/4)) + 2^(5/2)*zeta(3)^(1/4)*n^(3/4)/sqrt(3*Pi) - n) * n^(n - 1/8) / (2^(3/4) * Pi^(1/4)).

%t nmax = 25; CoefficientList[Series[Exp[Sum[DivisorSigma[2, k^2]/DivisorSigma[1, k^2]*x^k, {k, 1, nmax}]], {x, 0, nmax}], x] * Range[0, nmax]!

%Y Cf. A057660.

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, Nov 02 2024