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 A127534 #14 Jul 22 2022 08:36:21
%S A127534 0,1,9,65,442,2940,19380,127281,834900,5476185,35937525,236030652,
%T A127534 1551652424,10210456360,67254204696,443410005585,2926078447656,
%U A127534 19325957314755,127746785056275,845069382939705,5594334252541650
%N A127534 Number of jumps in all even trees with 2n edges.
%C A127534 An even tree is an ordered tree in which each vertex has an even outdegree. In the preorder traversal of an ordered tree, any transition from a node at a deeper level to a node on a strictly higher level is called a jump.
%C A127534 The Krandick reference considers jumps in full binary trees.
%H A127534 W. Krandick, <a href="https://doi.org/10.1016/j.cam.2003.08.018">Trees and jumps and real roots</a>, J. Computational and Applied Math., 162, 2004, 51-55.
%F A127534 a(n)=(n-1)(4n-3)C(3n,n)/[3(2n+1)(3n-1)].
%F A127534 D-finite with recurrence 8*n*(2*n+1)*a(n) -2*(136*n-69)*(n-1)*a(n-1) +5*(263*n^2-893*n+750)*a(n-2) -156*(3*n-8)*(3*n-10)*a(n-3)=0. - _R. J. Mathar_, Jul 22 2022
%p A127534 seq((n-1)*(4*n-3)*binomial(3*n,n)/3/(2*n+1)/(3*n-1),n=1..24);
%t A127534 Table[((n-1)(4n-3)Binomial[3n,n])/(3(2n+1)(3n-1)),{n,30}] (* _Harvey P. Dale_, Sep 29 2013 *)
%Y A127534 Cf. A127535, A127536.
%K A127534 nonn
%O A127534 1,3
%A A127534 _Emeric Deutsch_, Jan 19 2007