A105948 a(n) = C(n+5,5) * C(n+7,7).

1, 48, 756, 6720, 41580, 199584, 792792, 2718144, 8281845, 22902880, 58402344, 139007232, 311800944, 664191360, 1352103840, 2644114176, 4988699793, 9114302736, 16175074300, 27959131200, 47181033900, 77886151200, 126001769400, 200078424000, 312275179125

Offset: 0

Author

Zerinvary Lajos, Apr 27 2005

Keywords

• easy
• nonn

Examples

			If n=0 then C(0+7,0)*C(0+5,5) = C(7,0)*C(5,5) = 1*1 = 1.
If n=12 then C(12+7,12)*C(12+5,5) = C(19,12)*C(17,5) = 50388*6188 = 311800944.
		

Links

• T. D. Noe, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).

Crossrefs

Cf. A062196.

Programs

Magma

A105948:= func< n | Binomial(n+5,5)*Binomial(n+7,7) >;
[A105948(n): n in [0..40]]; // G. C. Greubel, Feb 22 2025

Mathematica

Table[Binomial[n+7,n]Binomial[n+5,5],{n,0,30}] (* Harvey P. Dale, Apr 08 2019 *)

SageMath

def A105948(n): return binomial(n+5,5)*binomial(n+7,7)
print([A105948(n) for n in range(41)]) # G. C. Greubel, Feb 22 2025

Formula

G.f.: (1 + 35*x + 210*x^2 + 350*x^3 + 175*x^4 + 21*x^5)/ (1-x)^13. - Colin Barker, Jan 29 2013

From Amiram Eldar, Sep 06 2022: (Start)

Sum_{n>=0} 1/a(n) = 1225*Pi^2 - 1740851/144.

Sum_{n>=0} (-1)^n/a(n) = 35*Pi^2/6 - 3584*log(2)/3 + 61719/80. (End)