This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A299429 #10 Sep 05 2025 02:01:43
%S A299429 1,1,7,117,3311,135408,7324878,495729741,40411916335,3861208027677,
%T A299429 423601805745460,52513639293534510,7263163165618323432,
%U A299429 1109176062938132317300,185415009041446934481180,33681956588219177374026429,6607825171826115567872400495,1392510451119380284814728497375
%N A299429 a(n) = binomial((n+1)*(2*n+1), n) / ((n+1)*(2*n+1)).
%C A299429 a(n) = A299428(n) / (n+1)^2.
%H A299429 Paul D. Hanna, <a href="/A299429/b299429.txt">Table of n, a(n) for n = 0..200</a>
%F A299429 a(n) ~ 2^(n-3/2) * exp(n + 5/4 - 19/(24*n)) * n^(n-5/2) / sqrt(Pi). - _Amiram Eldar_, Sep 05 2025
%t A299429 a[n_] := Binomial[(n+1)*(2*n+1), n]/((n+1)*(2*n+1)); Array[a, 20, 0] (* _Amiram Eldar_, Sep 05 2025 *)
%o A299429 (PARI) {a(n) = binomial((n+1)*(2*n+1), n)/((n+1)*(2*n+1)) }
%o A299429 for(n=0,20,print1(a(n),", "))
%Y A299429 Cf. A299427, A299428.
%K A299429 nonn,changed
%O A299429 0,3
%A A299429 _Paul D. Hanna_, Feb 19 2018