A378613 a(n) = Sum_{k=0..n} binomial(4*n+k-1,k) * binomial(n-1,n-k).

1, 4, 44, 532, 6748, 88024, 1169444, 15738328, 213842716, 2927097712, 40302226944, 557565134196, 7744326799684, 107925260553088, 1508352084699224, 21132667178858512, 296716493251706652, 4174006026061733232, 58816013334014598032, 830025065117154066064, 11729345524163083673648

Offset

0,2

Links

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

Formula

a(n) = [x^n] 1/(1 - x/(1 - x))^(4*n).

a(n) = (1/8)^n * [x^(4*n)] 4/(1 - x/(1 - x))^n for n > 0.

Prog

(PARI) a(n) = sum(k=0, n, binomial(4*n+k-1, k)*binomial(n-1, n-k));

Crossrefs

Cf. A002002, A378611, A378612.

Cf. A378610.

Sequence in context: A082779 A223053 A222288 * A053315 A005721 A103870

Adjacent sequences: A378610 A378611 A378612 * A378614 A378615 A378616

Keyword

nonn,new

Author

Seiichi Manyama, Dec 01 2024

Status

approved