A381877 G.f. A(x) satisfies A(x) = C(x) / (1 - x*A(x))^4, where C(x) is the g.f. of A000108.

1, 5, 36, 307, 2891, 29029, 304716, 3303712, 36708842, 415818822, 4783832314, 55743318579, 656528284027, 7802975428711, 93467830304056, 1127239608233884, 13676060532043690, 166800618473750824, 2043978275887704674, 25152767272402722288, 310703538187552229521

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Formula

a(n) = Sum_{k=0..n} binomial(n+k+1,k) * binomial(5*n-5*k+3,n-k)/(n+k+1).

a(n) = binomial(3 + 5*n, n)*hypergeom([-3/4-n, -1/2-n, -1/4-n, -n, 1+n], [-3/5-n, -2/5-n, -1/5-n, 1/5-n], 2^8/5^5)/(1 + n). - Stefano Spezia, Mar 09 2025

Prog

(PARI) a(n) = sum(k=0, n, binomial(n+k+1, k)*binomial(5*n-5*k+3, n-k)/(n+k+1));

Crossrefs

Cf. A129442, A381875, A381876.

Cf. A000108, A381861.

Sequence in context: A246510 A365754 A341961 * A278576 A286765 A267980

Adjacent sequences: A381874 A381875 A381876 * A381878 A381879 A381880

Keyword

nonn

Author

Seiichi Manyama, Mar 09 2025

Status

approved