OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..299
FORMULA
a(n) = Sum_{k=0..n} k^(2*n-k).
a(n) ~ sqrt(Pi) * 2^(1 + 2*n - 2*n/LambertW(2*exp(1)*n)) * (n/LambertW(2*exp(1)*n))^(1/2 + 2*n - 2*n/LambertW(2*exp(1)*n)) / sqrt(1 + LambertW(2*exp(1)*n)). - Vaclav Kotesovec, Dec 04 2021
MATHEMATICA
Join[{1}, Table[Sum[k^(2*n - k), {k, 0, n}], {n, 1, 20}]] (* Vaclav Kotesovec, Dec 04 2021 *)
PROG
(PARI) a(n, t=2) = sum(k=0, n, k^(t*(n-k)+k));
(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k*x)^k/(1-k^2*x)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Dec 03 2021
STATUS
approved