OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
G.f.: (1 -5*x +31*x^2 +21*x^3)/(1-x)^5. - R. J. Mathar, Feb 06 2017
E.g.f.: (1 - x + 11*x^2 + 12*x^3 + 2*x^4)*exp(x). - G. C. Greubel, Mar 05 2020
From Amiram Eldar, Mar 11 2022: (Start)
Sum_{n>=2} 1/a(n) = (Pi/sqrt(2))*cot(Pi/sqrt(2)) + 7/4.
Sum_{n>=2} (-1)^n/a(n) = (Pi/sqrt(2))*cosec(Pi/sqrt(2)) - 11/4. (End)
MAPLE
seq( (n^2 -1)*(2*n^2 -1), n=0..40); # G. C. Greubel, Mar 05 2020
MATHEMATICA
Table[(n^2 -1)*(2*n^2 -1), {n, 0, 40}] (* G. C. Greubel, Mar 05 2020 *)
LinearRecurrence[{5, -10, 10, -5, 1}, {1, 0, 21, 136, 465}, 40] (* Harvey P. Dale, Aug 24 2020 *)
PROG
(PARI) vector(41, n, my(m=n-1); (m^2 -1)*(2*m^2 -1)) \\ G. C. Greubel, Mar 05 2020
(Magma) [(n^2 -1)*(2*n^2 -1): n in [0..40]]; // G. C. Greubel, Mar 05 2020
(Sage) [(n^2 -1)*(2*n^2 -1) for n in (0..40)] # G. C. Greubel, Mar 05 2020
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved