A379022 a(n) = Sum_{k=0..n} binomial(2*n+k-1,k) * binomial(2*n+k,n-k).

1, 4, 36, 370, 4012, 44824, 510498, 5892310, 68684540, 806715964, 9532070396, 113179713046, 1349276883346, 16140148109960, 193629588953214, 2328744593780590, 28068490664161756, 338960821947139640, 4100329281075440400, 49676100591186493156, 602654837914634224812

Offset

0,2

Links

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

Formula

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

Prog

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

Crossrefs

Cf. A262910, A379025, A379026.

Cf. A379021.

Sequence in context: A371772 A138736 A372461 * A266093 A198638 A358954

Adjacent sequences: A379018 A379019 A379021 * A379023 A379024 A379025

Keyword

nonn,new

Author

Seiichi Manyama, Dec 14 2024

Status

approved