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 A302734 #23 Feb 16 2025 08:33:53
%S A302734 0,0,1,6,32,186,1245,9588,83752,817980,8827745,104277450,1337781336,
%T A302734 18518728326,275087536717,4364152920456,73637731186160,
%U A302734 1316713607842968,24869730218182497,494752411594456110,10339913354716379440,226485946787802241650,5188447062121251600221
%N A302734 Number of paths in the n-path complement graph.
%H A302734 Andrew Howroyd, <a href="/A302734/b302734.txt">Table of n, a(n) for n = 1..200</a>
%H A302734 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphPath.html">Graph Path</a>
%H A302734 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PathComplementGraph.html">Path Complement Graph</a>
%F A302734 a(n) = (1/2)*Sum_{k=2..n} Sum_{i=1..k} Sum_{j=0..k-i} (-1)^(k-i)*i!*2^j*binomial(n+i-k, i)*binomial(i, j)*binomial(k-i-1, k-i-j). - _Andrew Howroyd_, Apr 21 2018
%F A302734 a(n) ~ n! / (2*exp(1)). - _Vaclav Kotesovec_, Apr 22 2018
%t A302734 Array[(1/2) Sum[Sum[Sum[(-1)^(k - i) i!*2^j*Binomial[# + i - k, i] Binomial[i, j] Binomial[k - i - 1, k - i - j], {j, 0, k - i}], {i, k}], {k, 2, #}] &, 23] (* _Michael De Vlieger_, Apr 21 2018 *)
%t A302734 Table[Sum[(-1)^(k - i) i! 2^j Binomial[n + i - k, i] Binomial[i, j] Binomial[k - i - 1, k - i - j], {k, 2, n}, {i, k}, {j, 0, k - i}]/2, {n, 20}] (* _Eric W. Weisstein_, Apr 23 2018 *)
%o A302734 (PARI) a(n)={sum(k=2, n, sum(i=1, k, sum(j=0, min(i, k-i), (-1)^(k-i)*i!*2^j*binomial(n+i-k, i)*binomial(i, j)*binomial(k-i-1, k-i-j))))/2} \\ _Andrew Howroyd_, Apr 21 2018
%Y A302734 Cf. A001266, A006184, A242522.
%K A302734 nonn
%O A302734 1,4
%A A302734 _Eric W. Weisstein_, Apr 12 2018
%E A302734 Terms a(15) and beyond from _Andrew Howroyd_, Apr 21 2018