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A019583 a(n) = n*(n-1)^4/2. 3
0, 0, 1, 24, 162, 640, 1875, 4536, 9604, 18432, 32805, 55000, 87846, 134784, 199927, 288120, 405000, 557056, 751689, 997272, 1303210, 1680000, 2139291, 2693944, 3358092, 4147200, 5078125, 6169176 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

a(n) = n(n-1)^4/2 is half the number of colorings of 5 points on a line with n colors. - R. H. Hardin, Feb 23 2002

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

M. Janjic and B. Petkovic, A Counting Function, arXiv 1301.4550 [math.CO], 2013.

FORMULA

Sum_{j>=2} 1/A019583(j) = hypergeom([1, 1, 1, 1, 1], [ 2, 2, 2, 3], 1) = -2 + 2*zeta(2) - 2*zeta(3) + 2*zeta(4). - Stephen Crowley, Jun 28 2009

G.f.: x^2*(1 + 18*x + 33*x^2 + 8*x^3)/(1 - x)^6. - Colin Barker, Feb 23 2012

MATHEMATICA

CoefficientList[Series[x^2*(1+18*x+33*x^2+8*x^3)/(1-x)^6, {x, 0, 40}], x] (* Vincenzo Librandi, Apr 20 2012 *)

PROG

(MAGMA) [n*(n-1)^4/2: n in [0..30]]; // Vincenzo Librandi, Apr 20 2012

CROSSREFS

Sequence in context: A136380 A250323 A250142 * A244908 A087887 A288486

Adjacent sequences:  A019580 A019581 A019582 * A019584 A019585 A019586

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified October 23 22:26 EDT 2017. Contains 293833 sequences.