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 A339987 #38 Mar 07 2023 03:41:16
%S A339987 1,4,90,8400,1426950,366153480,134292027870,67095690261600,
%T A339987 43893900947947050,36441011093916429000,37446160423265535041100,
%U A339987 46669357647008722700474400,69367722399061403579194432500,121238024532751529573125745790000,246171692450596203263023527657431250
%N A339987 The number of labeled graphs on 2n vertices that share the same degree sequence as any unrooted binary tree on 2n vertices.
%C A339987 An unrooted binary tree is a tree in which all non-leaf vertices have degree 3. With 2n vertices there will be n+1 leaves and n-1 internal vertices.
%H A339987 Andrew Howroyd, <a href="/A339987/b339987.txt">Table of n, a(n) for n = 1..100</a> (terms 1..40 from Atabey Kaygun)
%H A339987 Atabey Kaygun, <a href="https://kaygun.tumblr.com/post/637867244800573440/counting-graphs-with-a-prescribed-degree-sequence">Counting Graphs with a Prescribed Degree Sequence</a>.
%H A339987 Atabey Kaygun, <a href="/A339987/a339987_2.lisp.txt">Common LISP program that generates the sequence</a>.
%H A339987 M. Kauers and C. Koutschan, <a href="https://arxiv.org/abs/2303.02793">Some D-finite and some possibly D-finite sequences in the OEIS</a>, arXiv:2303.02793 [cs.SC], 2023.
%F A339987 Conjectured recurrence: 32*(1 + n)*(2 + n)*(1 + 2*n)*(3 + 2*n)*(5 + 2*n)*(7 + 2*n)*(9 + 2*n)*(11589 + 10844*n + 3300*n^2 + 328*n^3)*a(n) - 8*(2 + n)*(3 + 2*n)*(5 + 2*n)*(7 + 2*n)*(9 + 2*n)*(148119 + 232328*n + 129460*n^2 + 30664*n^3 + 2624*n^4)*a(n+1) - 16*(3 + n)*(5 + 2*n)*(7 + 2*n)*(9 + 2*n)*(341634 + 712135*n + 569267*n^2 + 219308*n^3 + 40852*n^4 + 2952*n^5)*a(n+2) + 8*(4 + n)*(7 + 2*n)*(9 + 2*n)*(527520 + 1057879*n + 818282*n^2 + 306380*n^3 + 55672*n^4 + 3936*n^5)*a(n+3) - 2*(5 + n)*(9 + 2*n)*(601452 + 1117119*n + 786236*n^2 + 264028*n^3 + 42472*n^4 + 2624*n^5)*a(n+4) + 3*(4 + n)*(6 + n)*(3717 + 5228*n + 2316*n^2 + 328*n^3)*a(n+5) = 0. - _Manuel Kauers_ and _Christoph Koutschan_, Mar 01 2023
%F A339987 Conjecture: a(n) ~ 2^(5*n - 1/2) * n^(2*n - 3/2) / (sqrt(Pi) * 3^(n-1) * exp(2*n + 21/16)), based on the recurrence by _Manuel Kauers_ and _Christoph Koutschan_. - _Vaclav Kotesovec_, Mar 07 2023
%o A339987 (PARI) \\ See Links in A295193 for GraphsByDegreeSeq.
%o A339987 a(n) = {if(n==1, 1, my(d=2*n-4, M=GraphsByDegreeSeq(n-1, 3, (p,r)-> subst(deriv(p),x,1) >= d-6*r), z=(2*n)!/(n-1)!); sum(i=1, matsize(M)[1], my(p=M[i,1], r=(subst(deriv(p), x, 1)-d)/2); M[i,2]*z / (2^polcoef(p,1) * 6^polcoef(p,0) * 2^r * r!)))} \\ _Andrew Howroyd_, Mar 01 2023
%Y A339987 Cf. A001147, A001190, A002829.
%K A339987 nonn
%O A339987 1,2
%A A339987 _Atabey Kaygun_, Dec 25 2020