OFFSET
0,2
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (18,-153,816,-3060,8568,-18564,31824,-43758,48620,-43758,31824,-18564,8568,-3060,816,-153,18,-1).
FORMULA
From Amiram Eldar, Aug 30 2022: (Start)
Sum_{n>=0} 1/a(n) = 33033*Pi^2 - 16431490141/50400.
Sum_{n>=0} (-1)^n/a(n) = 1171456*log(2)/105 - 11*Pi^2/2 - 1625274871/211680. (End)
EXAMPLE
If n=0 then C(0+6,6)*C(0+11,0+0) = C(6,6)*C(11,0) = 1*1 = 1.
If n=8 then C(8+6,6)*C(8+11,8+0) = C(14,6)*C(19,8) = 3003*75582 = 226972746.
MATHEMATICA
a[n_] := Binomial[n + 6, 6] * Binomial[n + 11, n]; Array[a, 25, 0] (* Amiram Eldar, Aug 30 2022 *)
PROG
(PARI) a(n)={binomial(n+6, 6) * binomial(n+11, n)} \\ Andrew Howroyd, Nov 08 2019
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Zerinvary Lajos, Apr 22 2005
EXTENSIONS
a(8) corrected and terms a(9) and beyond from Andrew Howroyd, Nov 08 2019
STATUS
approved