A107398 a(n) = binomial(n+7, 7) * binomial(n+9, 7).

36, 960, 11880, 95040, 566280, 2718144, 11042460, 39262080, 125147880, 364066560, 979945824, 2466996480, 5859116640, 13220570880, 28506855960, 59025960576, 117846969900, 227667211200, 426876021000, 778861512000, 1386019463400, 2410468632000, 4104188068500

Offset: 0

Author

Zerinvary Lajos, May 25 2005

Keywords

• easy
• nonn

Examples

			If n=0 then C(n+7,7)*C(n+9,7) = C(7,7)*C(9,7) = 1*36 = 36.
If n=4 then C(4+7,7)*C(4+9,7) = C(11,7)*C(13,7) = 330*1716 = 566280.
		

Links

• Andrew Howroyd, 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

A107398:= func< n | Binomial(n+7,7)*Binomial(n+9,7) >;
[A107398(n): n in [0..30]]; // G. C. Greubel, Feb 07 2025

Mathematica

a[n_] := Binomial[n + 7, 7] * Binomial[n + 9, 7]; Array[a, 25, 0] (* Amiram Eldar, Sep 01 2022 *)

PARI

a(n)={binomial(n+7, 7) * binomial(n+9, 7)} \\ Andrew Howroyd, Nov 08 2019

SageMath

def A107398(n): return binomial(n+7,7)*binomial(n+9,7)
print([A107398(n) for n in range(31)]) # G. C. Greubel, Feb 07 2025

Formula

From Amiram Eldar, Sep 01 2022: (Start)

Sum_{n>=0} 1/a(n) = 8085*Pi^2/2 - 12767311/320.

Sum_{n>=0} (-1)^n/a(n) = 245*Pi^2/4 - 580307/960. (End)

G.f.: 12*(3 + 35*x + 105*x^2 + 105*x^3 + 35*x^4 + 3*x^5)/(1-x)^15. - G. C. Greubel, Feb 07 2025

Extensions

a(3) corrected and terms a(8) and beyond from Andrew Howroyd, Nov 08 2019