A352147 - OEIS

%I #15 Mar 11 2022 08:33:18

%S 1,-2,8,-51,437,-4685,60299,-905583,15543989,-300163717,6440430159,

%T -152007707357,3913861488767,-109171084473763,3279401359094041,

%U -105546729767585411,3623462164916028569,-132169615185372857001,5104616345453966073403

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

%H Seiichi Manyama, <a href="/A352147/b352147.txt">Table of n, a(n) for n = 0..399</a>

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

%t m = 18; 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, ((-1)^k*(k-1)!-1)*binomial(n, k)*a(n-k)));

%Y Cf. A352138, A352139, A352146.

%K sign

%O 0,2

%A _Seiichi Manyama_, Mar 06 2022