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 A288035 #18 Feb 16 2025 08:33:47
%S A288035 1,12,135,2224,55725,2006316,98309827,6291829440,509638185369,
%T A288035 50963818537900,6166622043087231,887993574204562992,
%U A288035 150070914040571147845,29413899151951944980364,6618127309189187620585275,1694240591152432030869834496,489635530843052856921382174257
%N A288035 Number of (undirected) paths in the complete bipartite graph K_n,n.
%H A288035 Andrew Howroyd, <a href="/A288035/b288035.txt">Table of n, a(n) for n = 1..50</a>
%H A288035 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CompleteBipartiteGraph.html">Complete Bipartite Graph</a>
%H A288035 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphPath.html">Graph Path</a>
%F A288035 a(n) = Sum_{k=2..2*n} n!^2/((n-ceiling(k/2))!*(n-floor(k/2))!). - _Andrew Howroyd_, Jun 10 2017
%F A288035 a(n) = n!^2 * Sum_{k=0..n-1} (1 + k)/(k!^2). - _Andrew Howroyd_, Feb 24 2023
%t A288035 Table[Sum[(n!)^2/((n - Ceiling[k/2])! (n - Floor[k/2])!), {k, 2, 2 n}], {n, 20}] (* _Eric W. Weisstein_, Jun 13 2017 *)
%t A288035 Table[n!^2 (BesselI[0, 2] + BesselI[1, 2] - HypergeometricPFQRegularized[{1}, {1 + n, 1 + n}, 1]) - n HypergeometricPFQ[{1}, {n, 1 + n}, 1], {n, 20}] // FunctionExpand (* _Eric W. Weisstein_, Jun 13 2017 *)
%o A288035 (PARI) a(n) = sum(k=2, 2*n, n!^2/((n-(k+1)\2)!*(n-k\2)!)); \\ _Andrew Howroyd_, Jun 10 2017
%o A288035 (PARI) a(n) = n!^2*sum(k=0, n-1, (1 + k)/(k!)^2) \\ _Andrew Howroyd_, Feb 24 2023
%Y A288035 Main diagonal of A307027 and A360850.
%Y A288035 Cf. A070968, A048617, A010790.
%K A288035 nonn
%O A288035 1,2
%A A288035 _Eric W. Weisstein_, Jun 04 2017
%E A288035 Terms a(8) and beyond from _Andrew Howroyd_, Jun 10 2017