A104671 a(n) = binomial(n+3,n)*binomial(n+8,n).

1, 36, 450, 3300, 17325, 72072, 252252, 772200, 2123550, 5348200, 12514788, 27511848, 57316350, 113954400, 217443600, 400096224, 712671399, 1232995500, 2077825750, 3418915500, 5504453955, 8687301480, 13461727500, 20510685000, 30766027500, 45484495056

Offset: 0

Author

Zerinvary Lajos, Apr 22 2005

Keywords

• nonn
• easy

Examples

			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.
		

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).

Crossrefs

Cf. A062190.

Programs

Magma

A104671:= func< n | Binomial(n+3,n)*Binomial(n+8,n) >;
[A104671(n): n in [0..30]]; // G. C. Greubel, Mar 01 2025

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 *)

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

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)

Extensions

a(12) corrected by Colin Barker, Jun 06 2012

More terms and a(7), a(15) corrected by Bruno Berselli, Jun 06 2012