A104679 a(n) = C(n+5,5)*C(n+10,5).

252, 2772, 16632, 72072, 252252, 756756, 2018016, 4900896, 11027016, 23279256, 46558512, 88884432, 162954792, 288304632, 494236512, 823727520, 1338557220, 2125943820, 3307023720, 5047562520, 7571343780, 11176745580, 16257084480, 23325382080, 33044291280

Offset: 0

Author

Zerinvary Lajos, Apr 22 2005

Keywords

• easy
• nonn

Examples

			If n=0 then C(0+5,0+0)*C(0+10,5) = C(5,0)*C(10,5) = 1*252 = 252.
If n=4 then C(4+5,4+0)*C(4+10,5) = C(9,4)*C(14,5) = 126*2002 = 252252.
		

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

Crossrefs

Cf. A062190.

Programs

Magma

[Binomial(n+5,n)*Binomial(n+10,5): n in [0..30]]; // G. C. Greubel, Nov 25 2017

Mathematica

Table[Binomial[n+5,n]Binomial[n+10,5],{n,0,20}] (* Harvey P. Dale, Feb 06 2015 *)

PARI

Vec(252/(1-x)^11 + O(x^100)) \\ Colin Barker, Feb 07 2015

Formula

G.f.: 252 / (1-x)^11. - Colin Barker, Feb 07 2015

a(n) = A000389(n+5)*A000389(n+10) = 252*A001287(n+11). - R. J. Mathar, Nov 29 2015

From Amiram Eldar, Aug 30 2022: (Start)

Sum_{n>=0} 1/a(n) = 5/1134.

Sum_{n>=0} (-1)^n/a(n) = 1280*log(2)/63 - 447047/31752. (End)

Extensions

Corrected and extended by Harvey P. Dale, Feb 06 2015