A107397 a(n) = binomial(n+6, 6) * binomial(n+8, 6).

28, 588, 5880, 38808, 194040, 792792, 2774772, 8588580, 24048024, 61941880, 148660512, 335785632, 719540640, 1472290848, 2891999880, 5477788008, 10042611348, 17877713700, 30988037080, 52423371000, 86736850200, 140610670200, 223698793500, 349748200620, 538074154800

Offset

0,1

Links

Andrew Howroyd, 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).

Formula

From Amiram Eldar, Sep 01 2022: (Start)

Sum_{n>=0} 1/a(n) = 720*Pi^2 - 1740989/245.

Sum_{n>=0} (-1)^n/a(n) = 6144*log(2)/7 - 149046/245. (End)

Example

If n=0 then C(0+6,6)*C(0+8,6) = C(6,6)*C(8,6) = 1*28 = 28.
If n=6 then C(6+6,6)*C(6+8,6) = C(12,6)*C(14,6) = 924*3003 = 2774772.

Mathematica

a[n_] := Binomial[n + 6, 6] * Binomial[n + 8, 6]; Array[a, 25, 0] (* Amiram Eldar, Sep 01 2022 *)

Prog

(PARI) a(n)={binomial(n+6, 6) * binomial(n+8, 6)} \\ Andrew Howroyd, Nov 08 2019

Crossrefs

Cf. A062196.

Sequence in context: A240800 A281125 A234618 * A053110 A264459 A004371

Adjacent sequences: A107394 A107395 A107396 * A107398 A107399 A107400

Keyword

easy,nonn

Author

Zerinvary Lajos, May 25 2005

Extensions

a(3) corrected and terms a(11) and beyond from Andrew Howroyd, Nov 08 2019

Status

approved