A107399 a(n) = binomial(n+8,8)*binomial(n+10,8).

45, 1485, 22275, 212355, 1486485, 8281845, 38648610, 156434850, 563165460, 1837398420, 5512195260, 15380181180, 40281426900, 99773995860, 235181561670, 530311364550, 1149007956525, 2401177618125, 4855714738875, 9528883810875, 18191505457125

Offset: 0

Author

Zerinvary Lajos, May 25 2005

Keywords

• easy
• nonn

Examples

			If n=0 then C(0+8,8)*C(0+10,8) = C(8,8)*C(10,8) = 1*45 = 45.
If n=4 then C(7+8,8)*C(7+10,8) = C(15,8)*C(17,8) = 3003*12870 = 38648610.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (17,-136,680,-2380,6188,-12376,19448,-24310,24310,-19448,12376,-6188,2380,-680,136,-17,1).

Crossrefs

Cf. A062196.

Programs

Magma

A107399:= func< n | Binomial(n+8,8)*Binomial(n+10,8) >;
[A107399(n): n in [0..30]]; // G. C. Greubel, Feb 07 2025

Mathematica

Table[Binomial[n+8,8]Binomial[n+10,8],{n,0,20}] (* Harvey P. Dale, Apr 03 2019 *)

SageMath

def A107399(n): return binomial(n+8,8)*binomial(n+10,8)
print([A107399(n) for n in range(31)]) # G. C. Greubel, Feb 07 2025

Formula

From Amiram Eldar, Sep 08 2022: (Start)

Sum_{n>=0} 1/a(n) = 64064*Pi^2/3 - 2987552614/14175.

Sum_{n>=0} (-1)^n/a(n) = 57237184/14175 - 262144*log(2)/45. (End)

G.f.: 45*(1 + 16*x + 70*x^2 + 112*x^3 + 70*x^4 + 16*x^5 + x^6)/(1-x)^17. - G. C. Greubel, Feb 07 2025

Extensions

More terms from Harvey P. Dale, Apr 03 2019