A107395 a(n) = binomial(n+4,4)*binomial(n+6,4).

15, 175, 1050, 4410, 14700, 41580, 103950, 235950, 495495, 975975, 1821820, 3248700, 5569200, 9224880, 14825700, 23197860, 35441175, 52997175, 77729190, 112015750, 158858700, 222007500, 306101250, 416830050, 561117375, 747325215, 985483800, 1287547800

Offset: 0

Author

Zerinvary Lajos, May 25 2005

Keywords

• easy
• nonn

Examples

			If n=0 then C(0+4,4)*C(0+6,4) = C(4,4)*C(6,4) = 1*15 = 15.
If n=9 then C(9+4,4)*C(9+6,4) = C(13,4)*C(15,4) = 715*1365 = 975975.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Crossrefs

Cf. A033987, A062196.

Programs

Magma

A107395:= func< n | Binomial(n+4,4)*Binomial(n+6,4) >;
[A107395(n): n in [0..30]]; // G. C. Greubel, Feb 09 2025

Mathematica

Table[Binomial[n+4,4]Binomial[n+6,4],{n,0,30}] (* Harvey P. Dale, Jun 07 2019 *)

SageMath

def A107395(n): return binomial(n+4,4)*binomial(n+6,4)
print([A107395(n) for n in range(31)]) # G. C. Greubel, Feb 09 2025

Formula

From Amiram Eldar, Sep 06 2022: (Start)

Sum_{n>=0} 1/a(n) = 16*Pi^2 - 3946/25.

Sum_{n>=0} (-1)^n/a(n) = 1776/25 - 512*log(2)/5. (End)

G.f.: 5*(3 + 8*x + 3*x^2)/(1-x)^9. - G. C. Greubel, Feb 09 2025

Extensions

More terms from Harvey P. Dale, Jun 07 2019