OFFSET
0,1
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).
FORMULA
From Amiram Eldar, Sep 01 2022: (Start)
Sum_{n>=0} 1/a(n) = 720*Pi^2 - 1740989/245.
Sum_{n>=0} (-1)^n/a(n) = 6144*log(2)/7 - 149046/245. (End)
EXAMPLE
If n=0 then C(0+6,6)*C(0+8,6) = C(6,6)*C(8,6) = 1*28 = 28.
If n=6 then C(6+6,6)*C(6+8,6) = C(12,6)*C(14,6) = 924*3003 = 2774772.
MATHEMATICA
a[n_] := Binomial[n + 6, 6] * Binomial[n + 8, 6]; Array[a, 25, 0] (* Amiram Eldar, Sep 01 2022 *)
PROG
(PARI) a(n)={binomial(n+6, 6) * binomial(n+8, 6)} \\ Andrew Howroyd, Nov 08 2019
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Zerinvary Lajos, May 25 2005
EXTENSIONS
a(3) corrected and terms a(11) and beyond from Andrew Howroyd, Nov 08 2019
STATUS
approved