OFFSET
1,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -5, 1).
FORMULA
a(n) = 7*C(n + 2, 4) + C(n + 1, 2).
G.f.: x*(-1-x^2-5*x)/(x-1)^5. - Maksym Voznyy (voznyy(AT)mail.ru), Aug 10 2009; adapted to the offset by Vincenzo Librandi, Sep 06 2013
Sum_{n>=1} 1/a(n) = 30 + 4*sqrt(21/5)*Pi*tan(sqrt(15/7)*Pi/2). - Amiram Eldar, Aug 23 2022
MATHEMATICA
CoefficientList[Series[(-1 - x^2 - 5 x) / (x - 1)^5, {x, 0, 40}], x] (* Vincenzo Librandi, Sep 06 2013 *)
LinearRecurrence[{5, -10, 10, -5, 1}, {1, 10, 41, 115, 260}, 40] (* Harvey P. Dale, Dec 27 2022 *)
PROG
(PARI) a(n) = 7*binomial(n + 2, 4) + binomial(n + 1, 2); \\ Michel Marcus, Sep 05 2013
(Magma) [7*Binomial(n+2, 4)+Binomial(n+1, 2): n in [1..40]]; // Vincenzo Librandi, Sep 06 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Albert Rich (Albert_Rich(AT)msn.com)
STATUS
approved