The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A019583 a(n) = n*(n-1)^4/2. 4
 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, 7440174, 8912512, 10609215, 12555000, 14776336, 17301504, 20160657 (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 Milan Janjic and Boris Petkovic, A Counting Function, arXiv 1301.4550 [math.CO], 2013. Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1). FORMULA Sum_{j>=2} 1/a(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 From Amiram Eldar, Feb 13 2023: (Start) a(n) = A101362(n-1)/2. Sum_{n>=2} (-1)^n/a(n) = 2 + Pi^2/6 + 7*Pi^4/360 - 4*log(2) - 3*zeta(3)/2. (End) 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 *) a[n_] := n*(n - 1)^4/2; Array[a, 30, 0] (* Amiram Eldar, Feb 13 2023 *) PROG (Magma) [n*(n-1)^4/2: n in [0..30]]; // Vincenzo Librandi, Apr 20 2012 CROSSREFS Cf. A101362. 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 12 05:07 EDT 2024. Contains 375842 sequences. (Running on oeis4.)