OFFSET
0,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
FORMULA
G.f.: (1 + 14*x + 21*x^2)/(1-x)^10. - Colin Barker, Mar 18 2012
From Amiram Eldar, Aug 30 2022: (Start)
Sum_{n>=0} 1/a(n) = 49*Pi^2/3 - 288281/1800.
Sum_{n>=0} (-1)^n/a(n) = 448*log(2)/3 - 35*Pi^2/6 - 1799/40. (End)
EXAMPLE
If n=0 then C(2+0,2)*C(7+0,0+0) = C(2,2)*C(7,0) = 1*1 = 1;
if n=6 then C(2+6,2)*C(7+6,0+6) = C(8,2)*C(13,6) = 28*1716 = 48048.
MAPLE
[seq(stirling2(n+1, n)*binomial(n+6, 7), n=1..25)]; # Zerinvary Lajos, Dec 06 2006
MATHEMATICA
a[n_] := Binomial[n + 2, 2] * Binomial[n + 7, 7]; Array[a, 25, 0] (* Amiram Eldar, Aug 30 2022 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Zerinvary Lajos, Apr 22 2005
EXTENSIONS
Corrected and extended by Don Reble, Nov 21 2006
STATUS
approved