A299429 a(n) = binomial((n+1)*(2*n+1), n) / ((n+1)*(2*n+1)).

1, 1, 7, 117, 3311, 135408, 7324878, 495729741, 40411916335, 3861208027677, 423601805745460, 52513639293534510, 7263163165618323432, 1109176062938132317300, 185415009041446934481180, 33681956588219177374026429, 6607825171826115567872400495, 1392510451119380284814728497375

Offset

0,3

Comments

a(n) = A299428(n) / (n+1)^2.

Links

Paul D. Hanna, Table of n, a(n) for n = 0..200

Formula

a(n) ~ 2^(n-3/2) * exp(n + 5/4 - 19/(24*n)) * n^(n-5/2) / sqrt(Pi). - Amiram Eldar, Sep 05 2025

Mathematica

a[n_] := Binomial[(n+1)*(2*n+1), n]/((n+1)*(2*n+1)); Array[a, 20, 0] (* Amiram Eldar, Sep 05 2025 *)

Prog

(PARI) {a(n) = binomial((n+1)*(2*n+1), n)/((n+1)*(2*n+1)) }
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A299427, A299428.

Sequence in context: A050285 A096760 A178791 * A297308 A077394 A009696

Adjacent sequences: A299426 A299427 A299428 * A299430 A299431 A299432

Keyword

nonn

Author

Paul D. Hanna, Feb 19 2018

Status

approved