OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..339
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
E.g.f.: sqrt( -LambertW(-2*x*exp(2*x)) / (2*x) ) = exp( x - LambertW(-2*x*exp(2*x))/2 ).
a(n) = Sum_{k=0..n} (2*k+1)^(n-1) * binomial(n,k) = 2^n * A202617(n).
a(n) ~ sqrt(1 + 1/LambertW(exp(-1))) * 2^(n-1) * n^(n-1) / (exp(n) * LambertW(exp(-1))^n). - Vaclav Kotesovec, Nov 10 2023
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(-2*x*exp(2*x))/2)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 01 2023
STATUS
approved