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

0, 7, 2902, 14872877, 1057937802444, 1139547636041211251, 19276901022645375031039586, 5187230738913145148610293591969497, 22294621657566842766129181417308087584893464, 1532378628985463601567919431617165851656712130496565087

Offset: 1

Author

Eric W. Weisstein, Dec 24 2017

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..25
• Eric Weisstein's World of Mathematics, Cocktail Party Graph
• Eric Weisstein's World of Mathematics, Edge Cover

Programs

Mathematica

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)}];
Array[a, 10] (* Jean-François Alcover, Dec 27 2017, after Andrew Howroyd *)

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

Formula

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

Extensions

Terms a(5) and beyond from Andrew Howroyd, Dec 27 2017