OFFSET
0,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
FORMULA
G.f.: (15*x^4+80*x^3+90*x^2+24*x+1) / (1-x)^11. [Colin Barker, Jan 28 2013]
From Wesley Ivan Hurt, Jan 27 2022: (Start)
a(n) = (17280 + 78336*n + 152376*n^2 + 167780*n^3 + 116150*n^4 + 52983*n^5 +
16173*n^6 + 3270*n^7 + 420*n^8 + 31*n^9 + n^10)/17280.
a(n) = 11*a(n-1)-55*a(n-2)+165*a(n-3)-330*a(n-4)+462*a(n-5)-462*a(n-6)+330*a(n-7)-165*a(n-8)+55*a(n-9)-11*a(n-10)+a(n-11). (End)
From Amiram Eldar, Sep 08 2022: (Start)
Sum_{n>=0} 1/a(n) = 224*Pi^2 - 55244/25.
Sum_{n>=0} (-1)^n/a(n) = 12*Pi^2 + 512*log(2)/5 - 4711/25. (End)
EXAMPLE
If n=0 then C(0+6,0)*C(0+4,4) = C(6,0)*C(4,4) = 1*1 = 1.
If n=10 then C(10+6,10)*C(10+4,4) = C(16,10)*C(14,4) = 8008*1001 = 8016008.
MATHEMATICA
Table[Binomial[n+6, n]Binomial[n+4, 4], {n, 0, 30}] (* or *) LinearRecurrence[ {11, -55, 165, -330, 462, -462, 330, -165, 55, -11, 1}, {1, 35, 420, 2940, 14700, 58212, 194040, 566280, 1486485, 3578575, 8016008}, 30] (* Harvey P. Dale, May 21 2014 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Zerinvary Lajos, Apr 27 2005
EXTENSIONS
Terms from a(8) onwards corrected by Colin Barker, Jan 28 2013
Second example corrected by Colin Barker, Jan 28 2013
STATUS
approved