cp's OEIS Frontend

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.

A288706 Number of (undirected) paths in the n-sun graph.

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%I A288706 #24 Jun 19 2025 10:09:57
%S A288706 108,614,3840,26937,211722,1852300,17900118,189670655,2188938928,
%T A288706 27349969842,368010246500,5307501200421,81699366763710,
%U A288706 1337244268935960,23195236251394954,425069874742963563,8207267847726907028,166543057722717660670,3543666872978746093608,78898851731990085876113
%N A288706 Number of (undirected) paths in the n-sun graph.
%H A288706 Andrew Howroyd, <a href="/A288706/b288706.txt">Table of n, a(n) for n = 3..200</a>
%H A288706 Andrew Howroyd, <a href="/A288706/a288706.txt">Derivation of formula</a>, Jun 2025.
%H A288706 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphPath.html">Graph Path</a>.
%H A288706 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SunGraph.html">Sun Graph</a>.
%o A288706 (PARI) a(n) = {my(s=sum(k=1, n, sum(i=0, min(k,n-k), binomial(k,i)*binomial(n-1,k+i-1)*2^i*(k-1)!*((5*k-2*i) - n*i/(k+i) + if(k>1, (i*(i+3) + 4*k*(k-1-i))/(k-1)))/k))); (2*(n-1) - 1 + s)*n/2} \\ _Andrew Howroyd_, Jun 17 2025
%Y A288706 Cf. A234627.
%K A288706 nonn
%O A288706 3,1
%A A288706 _Eric W. Weisstein_, Jun 13 2017
%E A288706 a(10) from _Eric W. Weisstein_, Sep 09 2017
%E A288706 a(11)-a(12) from _Eric W. Weisstein_, Mar 14 2019
%E A288706 a(13) onwards from _Andrew Howroyd_, Jun 17 2025