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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved