OFFSET
0,2
LINKS
T. D. Noe, 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
G.f.: -(21*x^5+175*x^4+350*x^3+210*x^2+35*x+1) / (x-1)^13. - Colin Barker, Jan 29 2013
From Amiram Eldar, Sep 06 2022: (Start)
Sum_{n>=0} 1/a(n) = 1225*Pi^2 - 1740851/144.
Sum_{n>=0} (-1)^n/a(n) = 35*Pi^2/6 - 3584*log(2)/3 + 61719/80. (End)
EXAMPLE
If n=0 then C(0+7,0)*C(0+5,5) = C(7,0)*C(5,5) = 1*1 = 1.
If n=12 then C(12+7,12)*C(12+5,5) = C(19,12)*C(17,5) = 50388*6188 = 311800944.
MATHEMATICA
Table[Binomial[n+7, n]Binomial[n+5, 5], {n, 0, 30}] (* or *) LinearRecurrence[ {13, -78, 286, -715, 1287, -1716, 1716, -1287, 715, -286, 78, -13, 1}, {1, 48, 756, 6720, 41580, 199584, 792792, 2718144, 8281845, 22902880, 58402344, 139007232, 311800944}, 30] (* Harvey P. Dale, Apr 08 2019 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Zerinvary Lajos, Apr 27 2005
STATUS
approved