OFFSET
0,2
LINKS
Winston de Greef, Table of n, a(n) for n = 0..420
FORMULA
a(n) = n! * Sum_{k=0..n} binomial(n+2*k+1,n-k)/k! = Sum_{k=0..n} (n+2*k+1)!/(3*k+1)! * binomial(n,k).
a(n) ~ 3^(5/8) * exp(-1/27 - 3^(3/4)*n^(1/4)/72 + sqrt(3*n)/6 + 4*3^(-3/4)*n^(3/4) - n) * n^(n + 3/8) / 6 * (1 + 63037 * 3^(1/4)/(69120 * n^(1/4))). - Vaclav Kotesovec, Mar 29 2023
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x/(1-x)^3)/(1-x)^2))
(PARI) a(n)=n! * sum(k=0, n, binomial(n+2*k+1, n-k)/k!) \\ Winston de Greef, Mar 18 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 18 2023
STATUS
approved