%I #15 Apr 28 2021 14:43:58

%S 1,2,4,9,23,70,244,1015,4605,25090,137516,963589,5832243,54685670,

%T 310755964,4567695283,15162041017,581160322338,-1133608829900,

%U 115627157052929,-1056546484541681,34518230044201062,-541838359813821916,14135169210980556655,-288911084512245360587

%N a(n) = n! * [x^n] exp(x)/(1 - log(1+x)).

%C Row sums of A291980.

%H G. C. Greubel, <a href="/A291981/b291981.txt">Table of n, a(n) for n = 0..450</a>

%F 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

%F 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

%p a_list := proc(n) exp(x)/(1 - log(1+x)): series(%, x, n+1):

%p seq(j!*coeff(%, x, j), j=0..n) end: a_list(24);

%t nmax = 20; CoefficientList[Series[E^x/(1 - Log[1+x]), {x, 0, nmax}], x] * Range[0, nmax]! (* _Vaclav Kotesovec_, Sep 18 2017 *)

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(x)/(1 - log(1+x)))) \\ _G. C. Greubel_, Aug 30 2018

%Y Cf. A291980.

%K sign

%O 0,2

%A _Peter Luschny_, Sep 16 2017