OFFSET
0,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).
FORMULA
From Harvey P. Dale, Feb 18 2012: (Start)
a(0)=1, a(1)=18, a(2)=126, a(3)=560, a(4)=1890, a(5)=5292, a(6)=12936, a(7)=28512, a(n)=8*a(n-1)-28*a(n-2)+56*a(n-3)-70*a(n-4)+56*a(n-5)- 28*a(n-6)+ 8*a(n-7)-a(n-8).
G.f.: (10*x*(x+1)+1)/(x-1)^8. (End)
From Amiram Eldar, Sep 08 2022: (Start)
Sum_{n>=0} 1/a(n) = 25*Pi^2/3 - 5845/72.
Sum_{n>=0} (-1)^n/a(n) = 205/8 - 5*Pi^2/2. (End)
EXAMPLE
If n=0 then C(0+2,2)*C(0+5,5) = C(2,2)*C(5,5) = 1*1 = 1.
If n=3 then C(3+2,2)*C(3+5,5) = C(5,2)*C(8,5) = 10*56 = 560.
MATHEMATICA
Table[Binomial[n+2, 2]Binomial[n+5, 5], {n, 0, 40}] (* or *) LinearRecurrence[ {8, -28, 56, -70, 56, -28, 8, -1}, {1, 18, 126, 560, 1890, 5292, 12936, 28512}, 40] (* Harvey P. Dale, Feb 18 2012 *)
PROG
(PARI) for(n=0, 29, print1(binomial(n+2, 2)*binomial(n+5, 5), ", "))
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Zerinvary Lajos, May 26 2005
EXTENSIONS
More terms from Rick L. Shepherd, May 27 2005
STATUS
approved