%I #14 Feb 11 2019 02:54:12
%S 1,4,63,1872,82775,4874688,358919022,31726703424,3273365223135,
%T 386120802767700,51255818495200660,7561964058268969440,
%U 1227474574989496660008,217398508335873934190800,41718377034325560258265500,8622580886584109407750765824,1909661474657747399115123743055,451173386162679212279972033149500
%N a(n) = binomial((n+1)*(2*n+1), n) * (n+1)/(2*n+1).
%C Main diagonal of square table A299427.
%H Seiichi Manyama, <a href="/A299428/b299428.txt">Table of n, a(n) for n = 0..310</a>
%F a(n) ~ 2^(n - 3/2) * exp(n + 5/4) * n^(n - 1/2) / sqrt(Pi). - _Vaclav Kotesovec_, Feb 19 2018
%o (PARI) {a(n) = binomial((n+1)*(2*n+1), n) * (n+1)/(2*n+1)}
%o for(n=0,20,print1(a(n),", "))
%Y Cf. A299427, A299429.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Feb 19 2018
%E a(15) corrected by _Seiichi Manyama_, Feb 10 2019