A295166 Chromatic invariant of the n-cocktail party graph.

2, 1, 11, 362, 21234, 1965624, 264398280, 48773612880, 11824686110160, 3646938237505920, 1394586705296776320, 647624841502298284800, 359025601255648673068800, 234214938700483636606233600, 177617896085186117264114611200, 154944426571409730022474894387200

Offset

1,1

Links

Andrew Howroyd, Table of n, a(n) for n = 1..100

Eric Weisstein's World of Mathematics, Chromatic Invariant

Eric Weisstein's World of Mathematics, Cocktail Party Graph

Formula

a(n) = Sum_{k=0..n} binomial(n,k)*(-1)^(n+k)*(n+k-2)! for n > 1. - Andrew Howroyd, Apr 22 2018

Mathematica

Join[{2}, Table[Sum[Binomial[n, k] (-1)^(k + n) (n + k - 2)!, {k, 0, n}], {n, 2, 20}]] (* Eric W. Weisstein, Apr 23 2018 *)
seq = Join[{2}, Table[-Gamma[n - 1] HypergeometricU[n - 1, 2 n, -1], {n, 2, 20}]] (* Eric W. Weisstein, Apr 23 2018 *)

Prog

(PARI) a(n)={if(n<2, [2][n], sum(k=0, n, binomial(n, k)*(-1)^(n+k)*(n+k-2)!))} \\ Andrew Howroyd, Apr 22 2018

Crossrefs

Sequence in context: A322513 A082272 A107049 * A345050 A285649 A074956

Adjacent sequences: A295163 A295164 A295165 * A295167 A295168 A295169

Keyword

nonn

Author

Eric W. Weisstein, Nov 16 2017

Extensions

a(16) from Andrew Howroyd, Apr 22 2018

Status

approved