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

Author

Paul D. Hanna, Feb 19 2018

Keywords

• nonn

Comments

Main diagonal of square table A299427.

Links

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

Crossrefs

Cf. A299427, A299429.

Programs

PARI

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

Formula

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

Extensions

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