A107421 a(n) = C(n+6,6)*C(n+9,9).

1, 70, 1540, 18480, 150150, 924924, 4624620, 19631040, 73002930, 243343100, 739763024, 2078672960, 5456516520, 13495999440, 31674284400, 70950397056, 152432493675, 315413948850, 630827897700, 1223211990000, 2305754601150, 4235059471500, 7595106655500

Offset

0,2

Links

T. D. Noe, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (16,-120,560,-1820,4368,-8008,11440,-12870,11440,-8008,4368,-1820,560,-120,16,-1).

Formula

G.f.: (84*x^6+756*x^5+1890*x^4+1680*x^3+540*x^2+54*x+1)/(x-1)^16. - Harvey P. Dale, Jan 30 2013

From Amiram Eldar, Sep 06 2022: (Start)

Sum_{n>=0} 1/a(n) = 11583*Pi^2 - 4481289621/39200.

Sum_{n>=0} (-1)^n/a(n) = 73728*log(2)/35 - 225*Pi^2/2 - 13673259/39200. (End)

Example

If n=0 then C(0+6,6)*C(0+9,9) = C(6,6)*C(9,9) = 1*1 = 1.
If n=7 then C(7+6,6)*C(7+9,9) = C(13,6)*C(16,9) = 1716*11440 = 19631040.

Mathematica

Table[Binomial[n+6, 6]Binomial[n+9, 9], {n, 0, 30}] (* Harvey P. Dale, Jan 30 2013 *)

Prog

(PARI) for(n=0, 29, print1(binomial(n+6, 6)*binomial(n+9, 9), ", "))

Crossrefs

Cf. A062145.

Sequence in context: A331351 A298973 A278548 * A076430 A006296 A047835

Adjacent sequences: A107418 A107419 A107420 * A107422 A107423 A107424

Keyword

easy,nonn

Author

Zerinvary Lajos, May 26 2005

Extensions

Corrected and extended by Rick L. Shepherd, May 27 2005

Status

approved