OFFSET
0,3
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
E.g.f.: exp( -LambertW(-x * (1+x)) ).
a(n) = n! * Sum_{k=0..n} (k+1)^(k-1) * binomial(k,n-k)/k!.
a(n) ~ sqrt(2 + 8*exp(-1) - 2*sqrt(1 + 4*exp(-1))) * 2^(n-1) * n^(n-1) / ((sqrt(1 + 4*exp(-1)) - 1)^n * exp(n - 3/2)). - Vaclav Kotesovec, May 03 2023
MATHEMATICA
nmax = 20; A[_] = 1;
Do[A[x_] = Exp[x*(1 + x)*A[x]] + O[x]^(nmax+1) // Normal, {nmax}];
CoefficientList[A[x], x]*Range[0, nmax]! (* Jean-François Alcover, Mar 04 2024 *)
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-x*(1+x)))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 02 2023
STATUS
approved