OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).
FORMULA
G.f.: (1+24*x+84*x^2+56*x^3)/(1-x)^12. - Bruno Berselli, Jun 06 2012
From Amiram Eldar, Aug 30 2022: (Start)
Sum_{n>=0} 1/a(n) = 144*Pi^2 - 1739736/1225.
Sum_{n>=0} (-1)^n/a(n) = 16*Pi^2 - 13312*log(2)/35 - 515202/1225. (End)
EXAMPLE
If n=0 then C(0+3,3)*C(0+8,0+0) = C(3,3)*C(8,0) = 1*1 = 1.
If n=6 then C(6+3,3)*C(6+8,6+0) = C(9,3)*C(14,6) = 84*3003 = 252252.
MATHEMATICA
Table[Binomial[n+3, 3]Binomial[n+8, n], {n, 0, 30}] (* or *)
LinearRecurrence[ {12, -66, 220, -495, 792, -924, 792, -495, 220, -66, 12, -1}, {1, 36, 450, 3300, 17325, 72072, 252252, 772200, 2123550, 5348200, 12514788, 27511848}, 30] (* Harvey P. Dale, Oct 05 2017 *)
PROG
(Magma)
A104671:= func< n | Binomial(n+3, n)*Binomial(n+8, n) >;
[A104671(n): n in [0..30]]; // G. C. Greubel, Mar 01 2025
(SageMath)
def A104671(n): return binomial(n+3, n)*binomial(n+8, n)
print([A104671(n) for n in range(31)]) # G. C. Greubel, Mar 01 2025
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Zerinvary Lajos, Apr 22 2005
EXTENSIONS
a(12) corrected by Colin Barker, Jun 06 2012
More terms and a(7), a(15) corrected by Bruno Berselli, Jun 06 2012
STATUS
approved