OFFSET
0,3
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
E.g.f.: A(x) = (-1/2) * LambertW(-2*x * exp(2*x)).
a(n) = Sum_{k=1..n} (2*k)^(n-1) * binomial(n,k) = 4^(n-1) * A100526(n).
a(n) ~ sqrt(1 + LambertW(exp(-1))) * 2^(n-1) * n^(n-1) / (LambertW(exp(-1))^n * exp(n)). - Vaclav Kotesovec, Feb 17 2023
MAPLE
A360548 := proc(n)
add((2*k)^(n-1)*binomial(n, k), k=1..n) ;
end proc:
seq(A360548(n), n=0..60) ; # R. J. Mathar, Mar 12 2023
PROG
(PARI) my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(-lambertw(-2*x*exp(2*x))/2)))
(PARI) a(n) = sum(k=1, n, (2*k)^(n-1)*binomial(n, k));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 11 2023
STATUS
approved