A107319 a(n) = C(n+8,8) * C(n+6,6).

1, 63, 1260, 13860, 103950, 594594, 2774772, 11042460, 38648610, 121671550, 350414064, 935402832, 2338507080, 5521090680, 12394285200, 26606398896, 54875697723, 109181751525, 210275965900, 393175282500, 715579014150, 1270517841450, 2205030964500, 3747302149500

Offset: 0

Author

Zerinvary Lajos, May 21 2005

Keywords

• easy
• nonn

Examples

			If n=0 then C(0+8,8)*C(0+6,6) = C(8,8)*C(6,6) = 1*1 = 1.
If n=6 then C(6+8,8)*C(6+6,6) = C(14,8)*C(12,6) = 3003*924 = 2774772.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (15,-105,455,-1365,3003,-5005,6435,-6435,5005,-3003,1365,-455,105,-15,1).

Crossrefs

Cf. A062196.

Programs

Magma

A107319:= func< n | Binomial(n+6,6)*Binomial(n+8,8) >;
[A107319(n): n in [0..40]]; // G. C. Greubel, Feb 22 2025

Mathematica

Table[Binomial[n+8,8]Binomial[n+6,6],{n,0,20}] (* Harvey P. Dale, Sep 02 2016 *)

SageMath

def A107319(n): return binomial(n+6,6)*binomial(n+8,8)
print([A107319(n) for n in range(41)]) # G. C. Greubel, Feb 22 2025

Formula

From Amiram Eldar, Sep 08 2022: (Start)

Sum_{n>=0} 1/a(n) = 6336*Pi^2 - 76602676/1225.

Sum_{n>=0} (-1)^n/a(n) = 1365906/1225 - 80*Pi^2 - 16384*log(2)/35. (End)

Extensions

More terms from Harvey P. Dale, Sep 02 2016