OFFSET
0,1
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (15,-105,455,-1365,3003,-5005,6435,-6435,5005,-3003,1365,-455,105,-15,1).
FORMULA
From Amiram Eldar, Sep 01 2022: (Start)
Sum_{n>=0} 1/a(n) = 8085*Pi^2/2 - 12767311/320.
Sum_{n>=0} (-1)^n/a(n) = 245*Pi^2/4 - 580307/960. (End)
EXAMPLE
If n=0 then C(n+7,7)*C(n+9,7) = C(7,7)*C(9,7) = 1*36 = 36.
If n=4 then C(4+7,7)*C(4+9,7) = C(11,7)*C(13,7) = 330*1716 = 566280.
MATHEMATICA
a[n_] := Binomial[n + 7, 7] * Binomial[n + 9, 7]; Array[a, 25, 0] (* Amiram Eldar, Sep 01 2022 *)
PROG
(PARI) a(n)={binomial(n+7, 7) * binomial(n+9, 7)} \\ Andrew Howroyd, Nov 08 2019
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Zerinvary Lajos, May 25 2005
EXTENSIONS
a(3) corrected and terms a(8) and beyond from Andrew Howroyd, Nov 08 2019
STATUS
approved