A378611 a(n) = Sum_{k=0..n} binomial(2*n+k-1,k) * binomial(n-1,n-k).

1, 2, 14, 104, 806, 6412, 51908, 425476, 3520070, 29332940, 245841284, 2070093632, 17499188924, 148414157816, 1262280506144, 10762045739644, 91951462167110, 787113739061260, 6749009521216052, 57954807274992208, 498334047795436276, 4290199618047230824

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Formula

a(n) = [x^n] 1/(1 - x/(1 - x))^(2*n).

a(n) = (1/2)^n * [x^(2*n)] 2/(1 - x/(1 - x))^n for n > 0.

a(n) = 2 * A259554(n) for n > 0.

Prog

(PARI) a(n) = sum(k=0, n, binomial(2*n+k-1, k)*binomial(n-1, n-k));

Crossrefs

Cf. A002002, A378612, A378613.

Cf. A211789, A259554.

Sequence in context: A286310 A295865 A355069 * A293044 A343818 A160780

Adjacent sequences: A378608 A378609 A378610 * A378612 A378613 A378614

Keyword

nonn

Author

Seiichi Manyama, Dec 01 2024

Status

approved