OFFSET
0,3
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..400
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
E.g.f. A(x) satisfies A(x) = x * (2*A(x) + exp(-A(x))).
E.g.f.: Series_Reversion( x / (2*x + exp(-x)) ).
a(n) = n! * Sum_{k=1..n} 2^(n-k) * (-k)^(k-1) * binomial(n-1,k-1)/k!.
MATHEMATICA
nmax=20; CoefficientList[InverseSeries[Series[x / (2*x + E^(-x)), {x, 0, nmax}], x], x] * Range[0, nmax]! (* Vaclav Kotesovec, Sep 20 2024 *)
PROG
(PARI) my(N=30, x='x+O('x^N)); concat(0, Vec(serlaplace(lambertw(x/(1-2*x)))))
(PARI) a(n) = n!*sum(k=1, n, 2^(n-k)*(-k)^(k-1)*binomial(n-1, k-1)/k!);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 10 2024
STATUS
approved