OFFSET
0,1
LINKS
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
FORMULA
From R. J. Mathar, Nov 29 2015: (Start)
G.f.: 4*(-14+14*x-6*x^2+x^3)/(x-1)^7. (End)
From Amiram Eldar, Aug 30 2022: (Start)
Sum_{n>=0} 1/a(n) = 109/4900.
Sum_{n>=0} (-1)^n/a(n) = 48*log(2)/35 - 2291/2450. (End)
EXAMPLE
If n=0 then C(0+3,0+0)*C(0+8,3) = C(3,0)*C(8,3) = 1*56 = 56.
If n=8 then C(8+3,8+0)*C(8+8,3) = C(11,8)*C(16,3) = 165*560 = 92400.
MATHEMATICA
a[n_] := Binomial[n+3, 3] * Binomial[n+8, 3]; Array[a, 30, 0] (* Amiram Eldar, Aug 30 2022 *)
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {56, 336, 1200, 3300, 7700, 16016, 30576}, 40] (* Harvey P. Dale, Jan 06 2023 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Zerinvary Lajos, Apr 22 2005
STATUS
approved