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 A103872 #20 Feb 16 2025 08:32:56
%S A103872 0,2,2,6,12,30,72,182,464,1206,3170,8426,22596,61074,166194,454950,
%T A103872 1251984,3461574,9611190,26787378,74916660,210178458,591347988,
%U A103872 1668172842,4717282752,13369522250,37970114702,108045430902
%N A103872 a(n) = 3*trinomial(n+1,0) - trinomial(n+2,0).
%C A103872 First differs from A059727 for n = 8.
%C A103872 Essentially twice A005043.
%H A103872 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TrinomialCoefficient.html">Trinomial Coefficient</a>
%p A103872 trinomial := n -> simplify(GegenbauerC(n,-n,-1/2)):
%p A103872 a := n -> 3*trinomial(n+1) - trinomial(n+2):
%p A103872 seq(a(n), n=0..27); # _Peter Luschny_, May 07 2016
%t A103872 Table[(4*2^n (2n + 3)!! (3 Hypergeometric2F1[-2 - n, -1 - n, -3/2 - n, 1/4] - 4 Hypergeometric2F1[-2 - n, -2 - n, -3/2 - n, 1/4]))/(n + 2)!, {n, 0, 20}] (* _Vladimir Reshetnikov_, May 07 2016 *)
%Y A103872 Cf. A005043, A059727.
%K A103872 nonn,easy
%O A103872 0,2
%A A103872 _Eric W. Weisstein_, Feb 19 2005