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 A277297 #9 Jul 24 2023 18:40:39
%S A277297 2,14,76,378,1808,8484,39446,182732,846248,3926338,18276832,85436832,
%T A277297 401313288,1894847846,8994916236,42931067910,206002472336,
%U A277297 993664391720,4817140123620,23464959242520,114820471485840,564248307992850,2783898831160512,13786409317705920,68509284536815640,341538385855855064,1707729163812908528
%N A277297 Diagonal of triangle A277295; a(n) = A277295(n+2,n).
%C A277297 G.f. G(x,y) of triangle A277295 satisfies:
%C A277297 (1) G(x,y) = x + G( y*G(x,y) + (1-y)*x, y)^2.
%C A277297 (2) G( x - y*G(x,y)^2, y) = x + (1-y)*G(x,y)^2.
%F A277297 a(n) = 2 * A291822(n) for n >= 1. - _Paul D. Hanna_, Jul 24 2023
%o A277297 (PARI) {A277295(n,k) = my(A=x); for(i=1, n, A = x + subst(A^2, x, y*A + (1-y)*x +x*O(x^n)) ); polcoeff(polcoeff(A,n,x),k,y)}
%o A277297 for(n=1,30,print1(A277295(n+2,n-1),", "))
%Y A277297 Cf. A277295, A277296, A277298, A277299, A291822.
%K A277297 nonn
%O A277297 1,1
%A A277297 _Paul D. Hanna_, Oct 11 2016