A352294 Expansion of e.g.f. 1/(exp(x) - x/(1 - x)).

1, 0, 1, 5, 29, 219, 1999, 21237, 257753, 3519863, 53408891, 891437073, 16231399381, 320172135555, 6801360675719, 154800119634989, 3758162030450993, 96941257338316911, 2647679298725738611, 76331396373264213417, 2316420658039348511981

Offset: 0

Author

Seiichi Manyama, Mar 11 2022

Keywords

• nonn

Crossrefs

Cf. A352292, A352295.

Programs

Mathematica

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

PARI

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

PARI

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

Formula

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

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