A285380 G.f.: 1/(1 - 1!*x/(1 - 2!*x/(1 - 3!*x/(1 - 4!*x/(1 - 5!*x/(1 - 6!*x/(1 - ...))))))), a continued fraction.
1, 1, 3, 21, 459, 48069, 31721355, 151932395493, 5929991210130219, 2103657835595933507013, 7506346835525189003011779147, 295743497615320848280307669164734117, 140189609286888251994538844205855399795958635
Offset: 0
Keywords
Examples
G.f.: A(x) = 1 + x + 3*x^2 + 21*x^3 + 459*x^4 + 48069*x^5 + 31721355*x^6 + 151932395493*x^7 + ...
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..43
Programs
-
Mathematica
nmax = 12; CoefficientList[Series[1/(1 + ContinuedFractionK[-k! x, 1, {k, 1, nmax}]), {x, 0, nmax}], x] -
PARI
a(n) = my(A=1+O(x)); for(i=1, n, A=1-(n-i+1)!*x/A); polcoef(1/A, n); \\ Seiichi Manyama, Apr 15 2021
Formula
a(n) ~ A000178(n) ~ BarnesG(n+2) ~ exp(1/12 - n - 3*n^2/4) * n^(5/12 + n + n^2/2) * (2*Pi)^((n+1)/2) / A, where A is the Glaisher-Kinkelin constant A074962. - Vaclav Kotesovec, Aug 26 2017