OFFSET
1,2
COMMENTS
Old name was: "Ratio of Sum of k^2-1 to sum of k made into an integer sequence: (n-1)*(2*n+5)".
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..5000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = 3*(n + 1)*( Sum_{k=1..n} k^2-1 )/ ( Sum_{k=1..n} k ) = (-1 + n)*(5 + 2*n).
G.f.: x^2*(9 - 5*x)/(1-x)^3. - R. J. Mathar, Nov 14 2007
a(n) = a(n-1) +4*n +1 for n>1, a(1)=0. - Vincenzo Librandi, Nov 23 2010
a(n) = n*(2n+7) with offset 0. - Michel Marcus, Jan 28 2015
8*a(n) + 49 = A016838(n). - Bruno Berselli, Jan 28 2015
E.g.f.: 5 + (2*x^2 + 5* x -5)*exp(x). - G. C. Greubel, Jul 21 2017
MATHEMATICA
Table[(n-1)(2n+5), {n, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 9, 22}, 50] (* Harvey P. Dale, Oct 02 2015 *)
PROG
(PARI) a(n)=(n-1)*(2*n+5) \\ Charles R Greathouse IV, Sep 24 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Roger L. Bagula, Jul 22 2007
STATUS
approved