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 A323229 #12 Sep 08 2022 08:46:23
%S A323229 1,2,5,16,57,211,793,3004,11441,43759,167961,646647,2496145,9657701,
%T A323229 37442161,145422676,565722721,2203961431,8597496601,33578000611,
%U A323229 131282408401,513791607421,2012616400081,7890371113951,30957699535777,121548660036301,477551179875953
%N A323229 a(n) = binomial(2*n, n+1) + 1.
%H A323229 G. C. Greubel, <a href="/A323229/b323229.txt">Table of n, a(n) for n = 0..1000</a>
%F A323229 Let G(x) = (1-3*x)/(2*(x-1)*x) + (I*(1-2*x))/(2*x*sqrt(4*x-1)) with Im(x) > 0, then a(n) = [x^n] G(x). The generating function G(x) satisfies the differential equation 6*x^3 - 4*x + 1 = (8*x^5 - 22*x^4 + 21*x^3 - 8*x^2 + x)*diff(G(x), x) + (4*x^4 - 14*x^3 + 17*x^2 - 8*x + 1)*G(x).
%F A323229 a(n) = A212382(2*n, n). - _Alois P. Heinz_, May 03 2019
%p A323229 aList := proc(len) local gf, ser; assume(Im(x) > 0);
%p A323229 gf := (1-3*x)/(2*(x-1)*x) + (I*(1-2*x))/(2*x*sqrt(4*x-1));
%p A323229 ser := series(gf, x, len+2):
%p A323229 seq(coeff(ser, x, n), n=0..len) end: aList(27);
%t A323229 Table[Binomial[2n, n+1] + 1, {n, 0, 26}]
%o A323229 (Magma) [Binomial(2*n, n+1) + 1: n in [0..30]]; // _G. C. Greubel_, Dec 26 2021
%o A323229 (Sage) [binomial(2*n, n+1) + 1 for n in (0..30)] # _G. C. Greubel_, Dec 26 2021
%Y A323229 Cf. A323230 (d=0), A260878 (d=1), this sequence (d=2).
%Y A323229 Cf. A212382.
%K A323229 nonn,easy
%O A323229 0,2
%A A323229 _Peter Luschny_, Feb 12 2019