A295171 Chromatic invariant of the n-crown graph.

1, 11, 328, 16369, 1181276, 116093641, 14916610346, 2428960220241, 489039354264712, 119323954705155265, 34701518665828422926, 11861024763916090258105, 4708209994260510940754540, 2148158302978435764574475817, 1116465105383647067485461486754

Offset

3,2

Links

Andrew Howroyd, Table of n, a(n) for n = 3..100

Eric Weisstein's World of Mathematics, Chromatic Invariant

Eric Weisstein's World of Mathematics, Crown Graph

Formula

a(n) = Sum_{k=2..2*n} Sum_{j=0..n} Sum_{i=0..k-j} (-1)^k*(k-2)!*binomial(n, j)*Stirling2(n-j, i)*Stirling2(n-j, k-j-i). - Andrew Howroyd, Apr 22 2018

Mathematica

Table[Sum[(-1)^k (k - 2)! Binomial[n, j] StirlingS2[n - j, i] StirlingS2[n - j, k - j - i], {k, 2, 2 n}, {j, 0, n}, {i, 0, k - j}], {n, 3, 20}] (* Eric W. Weisstein, Apr 23 2018 *)

Prog

(PARI) a(n)={sum(k=2, 2*n, (-1)^k*(k-2)!*sum(j=0, min(n, k), binomial(n, j)*sum(i=0, k-j, stirling(n-j, i, 2)*stirling(n-j, k-j-i, 2))))} \\ Andrew Howroyd, Apr 22 2018

Crossrefs

Sequence in context: A241127 A268551 A108274 * A254545 A160293 A084944

Adjacent sequences: A295168 A295169 A295170 * A295172 A295173 A295174

Keyword

nonn

Author

Eric W. Weisstein, Nov 16 2017

Extensions

Terms a(10) and beyond from Andrew Howroyd, Apr 22 2018

Status

approved