A104672 a(n) = binomial(n+4,n)*binomial(n+9,n).

1, 50, 825, 7700, 50050, 252252, 1051050, 3775200, 12033450, 34763300, 92470378, 229265400, 534952600, 1183859600, 2500601400, 5067885504, 9898213875, 18700431750, 34284124875, 61160599500, 106419443130, 180985447500, 301393121250, 492256440000, 789661372500

Offset: 0

Author

Zerinvary Lajos, Apr 22 2005

Keywords

• easy
• nonn

Examples

			If n=0 then C(0+4,4)*C(0+9,0+0) = C(4,4)*C(9,0) = 1*1 = 1.
If n=6 then C(6+4,4)*C(6+9,6+0) = C(10,4)*C(15,6) = 210*5005 = 1051050.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (14,-91,364,-1001,2002,-3003,3432,-3003,2002,-1001,364,-91,14,-1).

Crossrefs

Cf. A062190.

Programs

Magma

A104672:= func< n | Binomial(n+4,n)*Binomial(n+9,n) >;
[A104672(n): n in [0..30]]; // G. C. Greubel, Mar 01 2025

Mathematica

Table[Binomial[n+4,4]Binomial[n+9,n],{n,0,20}] (* Harvey P. Dale, Nov 15 2018 *)

SageMath

def A104672(n): return binomial(n+4,n)*binomial(n+9,n)
print([A104672(n) for n in range(31)]) # G. C. Greubel, Mar 01 2025

Formula

From Amiram Eldar, Aug 30 2022: (Start)

Sum_{n>=0} 1/a(n) = 990*Pi^2 - 38297957/3920.

Sum_{n>=0} (-1)^n/a(n) = 15*Pi^2 - 12288*log(2)/7 + 4193253/3920. (End)

G.f.: (1 + 36*x + 216*x^2 + 336*x^3 + 126*x^4)/(1-x)^14. - G. C. Greubel, Mar 01 2025

Extensions

More terms from Harvey P. Dale, Nov 15 2018