A352139 - OEIS

%I #23 Mar 10 2022 06:03:03

%S 1,-2,6,-27,161,-1205,10799,-113043,1351461,-18183781,271784079,

%T -4469044657,80160267791,-1557710354083,32597642189657,

%U -730897865864471,17480390183397209,-444198879957594857,11951585821669838395,-339434402344422296117

%N Expansion of e.g.f. 1/(exp(x) - log(1 - x)).

%H Seiichi Manyama, <a href="/A352139/b352139.txt">Table of n, a(n) for n = 0..421</a>

%F a(0) = 1; a(n) = -Sum_{k=1..n} ((k-1)! + 1) * binomial(n,k) * a(n-k).

%t m = 19; Range[0, m]! * CoefficientList[Series[1/(Exp[x] - Log[1 - x]), {x, 0, m}], x] (* _Amiram Eldar_, Mar 06 2022 *)

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(exp(x)-log(1-x))))

%o (PARI) a(n) = if(n==0, 1, -sum(k=1, n, ((k-1)!+1)*binomial(n, k)*a(n-k)));

%Y Cf. A352138, A352146, A352147.

%Y Cf. A006252, A038507.

%K sign

%O 0,2

%A _Seiichi Manyama_, Mar 06 2022