A291981 a(n) = n! * [x^n] exp(x)/(1 - log(1+x)).
1, 2, 4, 9, 23, 70, 244, 1015, 4605, 25090, 137516, 963589, 5832243, 54685670, 310755964, 4567695283, 15162041017, 581160322338, -1133608829900, 115627157052929, -1056546484541681, 34518230044201062, -541838359813821916, 14135169210980556655, -288911084512245360587
Offset: 0
Keywords
Links
- G. C. Greubel, Table of n, a(n) for n = 0..450
Crossrefs
Cf. A291980.
Programs
-
Maple
a_list := proc(n) exp(x)/(1 - log(1+x)): series(%, x, n+1): seq(j!*coeff(%, x, j), j=0..n) end: a_list(24);
-
Mathematica
nmax = 20; CoefficientList[Series[E^x/(1 - Log[1+x]), {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Sep 18 2017 *) -
PARI
x='x+O('x^30); Vec(serlaplace(exp(x)/(1 - log(1+x)))) \\ G. C. Greubel, Aug 30 2018
Formula
a(n) ~ n! * (-1)^(n+1) * exp(-1) / (log(n)^2 * n) * (1 - 2*(1 + gamma)/log(n)), where gamma is the Euler-Mascheroni constant (A001620). - Vaclav Kotesovec, Sep 18 2017
a(n) = 1 + Sum_{k=0..n-1} (-1)^(n-k-1) * binomial(n,k) * (n-k-1)! * a(k). - Ilya Gutkovskiy, Apr 28 2021
Comments