A107398 a(n) = binomial(n+7, 7) * binomial(n+9, 7).

36, 960, 11880, 95040, 566280, 2718144, 11042460, 39262080, 125147880, 364066560, 979945824, 2466996480, 5859116640, 13220570880, 28506855960, 59025960576, 117846969900, 227667211200, 426876021000, 778861512000, 1386019463400, 2410468632000, 4104188068500

Offset

0,1

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1000

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 01 2022: (Start)

Sum_{n>=0} 1/a(n) = 8085*Pi^2/2 - 12767311/320.

Sum_{n>=0} (-1)^n/a(n) = 245*Pi^2/4 - 580307/960. (End)

Example

If n=0 then C(n+7,7)*C(n+9,7) = C(7,7)*C(9,7) = 1*36 = 36.
If n=4 then C(4+7,7)*C(4+9,7) = C(11,7)*C(13,7) = 330*1716 = 566280.

Mathematica

a[n_] := Binomial[n + 7, 7] * Binomial[n + 9, 7]; Array[a, 25, 0] (* Amiram Eldar, Sep 01 2022 *)

Prog

(PARI) a(n)={binomial(n+7, 7) * binomial(n+9, 7)} \\ Andrew Howroyd, Nov 08 2019

Crossrefs

Cf. A062196.

Sequence in context: A011811 A167250 A218177 * A053111 A260855 A130563

Adjacent sequences: A107395 A107396 A107397 * A107399 A107400 A107401

Keyword

easy,nonn

Author

Zerinvary Lajos, May 25 2005

Extensions

a(3) corrected and terms a(8) and beyond from Andrew Howroyd, Nov 08 2019

Status

approved