A347795 Expansion of e.g.f. 1/(1 - x*exp(x)/(1 - 4*x*exp(x)/(1 - 9*x*exp(x)/(1 - 16*x*exp(x)/(1 - ...))))), a continued fraction.

1, 1, 12, 429, 37876, 6761065, 2136044046, 1089769282777, 840138009989496, 930785292596431665, 1424838078730777692250, 2919980132606043561607201, 7805899106468938819037737572, 26636112093062499073393688363737, 113900544542333346101951507567405622

Offset: 0

Author

Vaclav Kotesovec, Sep 14 2021

Keywords

• nonn

Crossrefs

Cf. A295240.

Programs

Mathematica

nmax = 20; CoefficientList[Series[1/(1 + ContinuedFractionK[-k^2*x*Exp[x], 1, {k, 1, nmax}]), {x, 0, nmax}], x] * Range[0, nmax]!

Formula

a(n) ~ 2^(4*n + 7/2) * n^(3*n + 1) / (exp(3*n) * Pi^(2*n)).