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 A019583 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 A019583[n+2]=denom((1/2)*n^5+3*n^4+7*n^3+8*n^2+(9/2)*n+1) [From Stephen Crowley, Jun 28 2009] LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 M. Janjic and B. Petkovic, A Counting Function, arXiv 1301.4550, 2013 FORMULA sum(1/A019583[j],j=2..infinity)=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] MAPLE with(combinat):a:=n->sum(sum(sum(binomial(n+2, 2), j=0..n), k=0..n), m=0..n): seq(a(n), n=-2..25); - Zerinvary Lajos, May 30 2007 a:=n->sum(n^2*sum(n, k=0..n-1), k=0..n)/2:seq(a(n), n=-1...26); - Zerinvary Lajos, Aug 01 2008 a:=n->sum(n^2*sum(n, k=0..n-1), k=0..n)/2:seq(a(n), n=-1...26); [Zerinvary Lajos, Aug 09 2008] 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 A223291 Adjacent sequences:  A019580 A019581 A019582 * A019584 A019585 A019586 KEYWORD nonn,easy AUTHOR EXTENSIONS hypergeometric zeta formula [Stephen Crowley, Jun 28 2009] STATUS approved

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