OFFSET
0,3
FORMULA
a(n) = 1/2 * Sum_{k=0..n} (n+k/2+1/2)^(n-1) * binomial(n,k).
a(n) ~ sqrt((1 + s)/(4 + 9*s)) * s^(2*n + 1) * (2 + 3*s)^n * n^(n-1) / (2^n * exp(n)), where s = 1.470103625022272111740158699814771551850270522048... is the root of the equation log(s) = (1 + s)/(2 + 3*s). - Vaclav Kotesovec, Apr 24 2024
PROG
(PARI) a(n) = sum(k=0, n, (n+k/2+1/2)^(n-1)*binomial(n, k))/2;
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 24 2024
STATUS
approved