A352294 - OEIS

%I #12 Jul 21 2022 07:34:51

%S 1,0,1,5,29,219,1999,21237,257753,3519863,53408891,891437073,

%T 16231399381,320172135555,6801360675719,154800119634989,

%U 3758162030450993,96941257338316911,2647679298725738611,76331396373264213417,2316420658039348511981

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

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

%F a(n) ~ n! * (1-r)^2 / ((1 - (1-r)*r) * r^(n+1)), where r = 0.65904606840740666... is the root of the equation exp(r)*(1-r) = r. - _Vaclav Kotesovec_, Jul 21 2022

%t m = 20; Range[0, m]! * CoefficientList[Series[1/(Exp[x] - x/(1 - x)), {x, 0, m}], x] (* _Amiram Eldar_, Mar 11 2022 *)

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

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

%Y Cf. A352292, A352295.

%K nonn

%O 0,4

%A _Seiichi Manyama_, Mar 11 2022