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 A126185 #7 Jul 22 2022 13:17:04
%S A126185 0,0,0,3,29,198,1180,6570,35196,184128,948516,4835295,24469005,
%T A126185 123174810,617662890,3088403955,15409111025,76755126600,381848749720,
%U A126185 1897825700385,9425387927295,46783757341050,232114595171200
%N A126185 Number of nonroot nodes of outdegree 2 in all hex trees with n edges.
%C A126185 A hex tree is a rooted tree where each vertex has 0, 1, or 2 children and, when only one child is present, it is either a left child, or a middle child, or a right child (name due to an obvious bijection with certain tree-like polyhexes; see the Harary-Read reference).
%H A126185 F. Harary and R. C. Read, <a href="https://doi.org/10.1017/S0013091500009135">The enumeration of tree-like polyhexes</a>, Proc. Edinburgh Math. Soc. (2) 17 (1970), 1-13.
%F A126185 a(n) = Sum_{k=0..floor((n-1)/2)} k*A126183(n,k).
%F A126185 G.f.= [(2-15z+30z^2-15z^3)sqrt(1-6z+5z^2)-(1-5z)(2-7z)(1-z)^2]/[2z^2*(1-6z+5z^2)].
%F A126185 D-finite with recurrence -(n+2)*(n-3)*a(n) +(7*n+1)*(n-2)*a(n-1) -(11*n-15)*(n-2)*a(n-2) +5*(n-2)*(n-3)*a(n-3)=0. - _R. J. Mathar_, Jul 22 2022
%p A126185 G:=((2-15*z+30*z^2-15*z^3)*sqrt(1-6*z+5*z^2)-(1-z)^2*(1-5*z)*(2-7*z))/2/z^2/(1-6*z+5*z^2):Gser:=series(G,z=0,31): seq(coeff(Gser,z,n),n=0..26);
%Y A126185 Cf. A126183.
%K A126185 nonn
%O A126185 0,4
%A A126185 _Emeric Deutsch_, Dec 19 2006