A299428 a(n) = binomial((n+1)*(2*n+1), n) * (n+1)/(2*n+1).

1, 4, 63, 1872, 82775, 4874688, 358919022, 31726703424, 3273365223135, 386120802767700, 51255818495200660, 7561964058268969440, 1227474574989496660008, 217398508335873934190800, 41718377034325560258265500, 8622580886584109407750765824, 1909661474657747399115123743055, 451173386162679212279972033149500

Offset

0,2

Comments

Main diagonal of square table A299427.

Links

Seiichi Manyama, Table of n, a(n) for n = 0..310

Formula

a(n) ~ 2^(n - 3/2) * exp(n + 5/4) * n^(n - 1/2) / sqrt(Pi). - Vaclav Kotesovec, Feb 19 2018

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, A299429.

Sequence in context: A177788 A293860 A349075 * A274392 A237644 A024256

Adjacent sequences: A299425 A299426 A299427 * A299429 A299430 A299431

Keyword

nonn

Author

Paul D. Hanna, Feb 19 2018

Extensions

a(15) corrected by Seiichi Manyama, Feb 10 2019

Status

approved