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.

A297029 Number of edge covers in the n-cocktail party graph.

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%I A297029 #12 Feb 16 2025 08:33:52
%S A297029 0,7,2902,14872877,1057937802444,1139547636041211251,
%T A297029 19276901022645375031039586,5187230738913145148610293591969497,
%U A297029 22294621657566842766129181417308087584893464,1532378628985463601567919431617165851656712130496565087
%N A297029 Number of edge covers in the n-cocktail party graph.
%H A297029 Andrew Howroyd, <a href="/A297029/b297029.txt">Table of n, a(n) for n = 1..25</a>
%H A297029 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CocktailPartyGraph.html">Cocktail Party Graph</a>
%H A297029 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EdgeCover.html">Edge Cover</a>
%F A297029 a(n) = Sum_{i=0..n} Sum_{j=0, 2*(n-i)} (-1)^(i+j)*binomial(n, i)*binomial(2*(n-i), j)*2^(binomial(2*n-j, 2)-i). - _Andrew Howroyd_, Dec 27 2017
%t A297029 a[n_] := Sum[(-1)^(i + j)*Binomial[n, i]*Binomial[2*(n - i), j] * 2^(Binomial[2*n - j, 2] - i), {i, 0, n}, {j, 0, 2*(n - i)}];
%t A297029 Array[a, 10] (* _Jean-François Alcover_, Dec 27 2017, after _Andrew Howroyd_ *)
%o A297029 (PARI) a(n)={sum(i=0, n, sum(j=0, 2*(n-i), (-1)^(i+j)*binomial(n, i)*binomial(2*(n-i), j)*2^(binomial(2*n-j, 2)-i)))} \\ _Andrew Howroyd_, Dec 27 2017
%K A297029 nonn
%O A297029 1,2
%A A297029 _Eric W. Weisstein_, Dec 24 2017
%E A297029 Terms a(5) and beyond from _Andrew Howroyd_, Dec 27 2017