A147859 Chromatic polynomial pi_n(z) of the helm graph H_n evaluated at z=n.

0, 0, 0, 5832, 1228800, 384375000, 153080202240, 77461492681776, 48745516577587200, 37439062705187626320, 34519165560000000000000, 37661140521028611405206520, 48018043198541202818460549120, 70773783408692477397888505288296, 119443378434420330312430518726819840

Offset

1,4

Comments

The helm graph H_n is the graph obtained from an n-wheel graph by adjoining a pendant edge at each node of the cycle.

Links

Table of n, a(n) for n=1..15.

J. A. Gallian, A dynamic survey of graph labeling, Elec. J. Combin., (2013), #DS6.

Eric W. Weisstein, Helm Graph

Formula

Pi_n(z) = z*((1-z)^n*(z-2)+(z-2)^n*(z-1)^n); a(n) = Pi_n(n).

Example

a(3) = 3 * ((1 - 3)^3 * (3 - 2) + (3 - 2)^3 * (3 - 1)^3) = 0.

Maple

P := proc(n, z) z*((1-z)^n*(z-2)+(z-2)^n*(z-1)^n) ; end: A147859 := proc(n) P(n, n) ; end: for n from 1 to 15 do printf("%d, ", A147859(n)) ; od: # R. J. Mathar, Jan 22 2009

Crossrefs

Sequence in context: A035903 A251189 A269185 * A269151 A269213 A114771

Adjacent sequences: A147856 A147857 A147858 * A147860 A147861 A147862

Keyword

easy,nonn

Author

Jonathan Vos Post, Nov 16 2008

Extensions

Corrected parentheses, definition and values R. J. Mathar, Jan 22 2009

Status

approved