OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..360
FORMULA
a(n) ~ 2^(2*n + 1/2) * r^(n+1) * n^n / (sqrt(1 + r^2) * exp(n) * (1 - r^2)^n), where r = 0.647918229029602749602061258113970414114660380467168496836586... is the positive root of the equation (1 + r) = (1 - r)*exp(1/r).
MATHEMATICA
Join[{1}, Table[Sum[Binomial[2*n, n-k]*k^n, {k, 0, n}], {n, 1, 20}]]
PROG
(PARI) a(n) = sum(k=0, n, binomial(2*n, n-k) * k^n); \\ Michel Marcus, Oct 03 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Oct 03 2021
STATUS
approved