OFFSET
0,2
FORMULA
a(n) = (1/(n+1)) * Sum_{k=0..n} 25^k * binomial(n/5+1/5,k) * binomial(k,n-k).
a(5*n+4) = 0 for n >= 0.
a(n) = 25^n*binomial((n+1)/5, n)*hypergeom([(1-n)/2, -n/2], [(6-4*n)/5], 4/25)/(n+1). - Stefano Spezia, Apr 18 2024
PROG
(PARI) a(n) = sum(k=0, n, 25^k*binomial(n/5+1/5, k)*binomial(k, n-k))/(n+1);
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Apr 15 2024
STATUS
approved