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 A306519 #10 Jan 30 2020 21:29:18
%S A306519 1,0,2,4,16,56,216,848,3424,14080,58816,248832,1064064,4591744,
%T A306519 19970432,87448832,385226240,1705979904,7590632448,33916934144,
%U A306519 152128126976,684702330880,3091429158912,13997970530304,63550155145216,289216809762816,1319185060069376,6029646893252608
%N A306519 Expansion of 2/(1 + 2*x + sqrt(1 - 4*x*(1 + x))).
%C A306519 Inverse binomial transform of A001003.
%F A306519 a(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(n,k)*A001003(k).
%F A306519 a(n) ~ 2^(n - 1/4) * (1 + sqrt(2))^(n - 1/2) / (sqrt(Pi) * n^(3/2)). - _Vaclav Kotesovec_, Feb 23 2019
%F A306519 D-finite with recurrence: (n+1)*a(n) +3*(-n+1)*a(n-1) +2*(-4*n+5)*a(n-2) +4*(-n+2)*a(n-3)=0. - _R. J. Mathar_, Jan 25 2020
%t A306519 nmax = 27; CoefficientList[Series[2/(1 + 2 x + Sqrt[1 - 4 x (1 + x)]), {x, 0, nmax}], x]
%t A306519 Table[Sum[(-1)^(n - k) Binomial[n, k] Hypergeometric2F1[1 - k, -k, 2, 2], {k, 0, n}], {n, 0, 27}]
%Y A306519 Cf. A001003, A005043, A052709, A118376, A174347.
%K A306519 nonn
%O A306519 0,3
%A A306519 _Ilya Gutkovskiy_, Feb 21 2019