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

0,2

Links

Table of n, a(n) for n=0..23.

Index entries for linear recurrences with constant coefficients, signature (15,-105,455,-1365,3003,-5005,6435,-6435,5005,-3003,1365,-455,105,-15,1).

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)

Example

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.

Mathematica

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

Crossrefs

Sequence in context: A230660 A132465 A202983 * A243214 A341569 A005463

Adjacent sequences: A107316 A107317 A107318 * A107320 A107321 A107322

Keyword

easy,nonn

Author

Zerinvary Lajos, May 21 2005

Extensions

More terms from Harvey P. Dale, Sep 02 2016

Status

approved