OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
Row sums from A163676: a(n) = Sum_{m=1..n} (4*m*n + 2*m + 2*n - 1).
G.f.: x*(7 + 8*x - 3*x^2)/(1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).
E.g.f.: x*(7 + 11*x + 2*x^2)*exp(x). - G. C. Greubel, Aug 02 2017
From Amiram Eldar, Feb 25 2023: (Start)
Sum_{n>=1} 1/a(n) = Pi^2/30 + 4*log(2)/25 - 92/375.
Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2/60 - Pi/25 -2*log(2)/25 + 52/375. (End)
MATHEMATICA
CoefficientList[Series[-x*(-7-8*x+3*x^2)/(x-1)^4, {x, 0, 40}], x] (* or *) LinearRecurrence[{4, -6, 4, -1}, {0, 7, 36, 99}, 50](* Vincenzo Librandi, Mar 06 2012 *)
Table[n^2(2n+5), {n, 0, 50}] (* Harvey P. Dale, Apr 10 2019 *)
PROG
(PARI) my(x='x+O('x^50)); concat([0], Vec(x*(7 +8*x -3*x^2)/(1 - x)^4)) \\ G. C. Greubel, Aug 02 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Aug 03 2009
EXTENSIONS
Edited, a(12) corrected - R. J. Mathar, Aug 05 2009
STATUS
approved