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