A107421 a(n) = binomial(n+6,6)*binomial(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

Author

Zerinvary Lajos, May 26 2005

Keywords

• easy
• nonn

Examples

			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.
		

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).

Crossrefs

Cf. A062145.

Programs

Magma

A107421:= func< n | Binomial(n+6,n)*Binomial(n+9,n) >;
[A107421(n): n in [0..40]]; // G. C. Greubel, Mar 09 2025

Mathematica

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

PARI

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

SageMath

def A107421(n): return binomial(n+6,n)*binomial(n+9,n)
print([A107421(n) for n in range(41)]) # G. C. Greubel, Mar 09 2025

Formula

G.f.: (1+54*x+540*x^2+1680*x^3+1890*x^4+756*x^5+84*x^6)/(1-x)^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)

Extensions

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