A105943 a(n) = binomial(n+7,7) * binomial(n+10,7).

120, 2640, 28512, 205920, 1132560, 5096520, 19631040, 66745536, 204787440, 576438720, 1507608960, 3700494720, 8593371072, 19004570640, 40244973120, 81980500800, 161264274600, 307350735120, 569168028000, 1026681084000, 1807851474000, 3113521983000

Offset: 0

Author

Zerinvary Lajos, Apr 27 2005

Keywords

• easy
• nonn

Examples

			If n=0 then C(0+7,0)*C(0+10,7) = C(7,0)*C(10,7) = 1*120 = 120.
If n=6 then C(6+7,6)*C(6+10,7) = C(13,6)*C(16,7) = 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 (15,-105,455,-1365,3003,-5005,6435,-6435,5005,-3003,1365,-455,105,-15,1).

Crossrefs

Cf. A062145.

Programs

Magma

A105943:= func< n | Binomial(n+7,7)*Binomial(n+10,7) >;
[A105943(n): n in [0..40]]; // G. C. Greubel, Mar 10 2025

Maple

A105943:=n->binomial(n+7,n)*binomial(n+10,7): seq(A105943(n), n=0..40); # Wesley Ivan Hurt, Apr 18 2017

Mathematica

Table[Binomial[n+7,n]Binomial[n+10,7],{n,0,30}] (* Harvey P. Dale, Nov 14 2011 *)

Python

A105943_list, m = [], [3432, -3432, 1320, 0]+[120]*11
for _ in range(10**2):
    A105943_list.append(m[-1])
    for i in range(14):
        m[i+1] += m[i] # Chai Wah Wu, Jan 24 2016

SageMath

def A105943(n): return binomial(n+7,7)*binomial(n+10,7)
print([A105943(n) for n in range(41)]) # G. C. Greubel, Mar 10 2025

Formula

G.f.: 24*(5 + 35*x + 63*x^2 +35*x^3 + 5*x^4)/(1-x)^15. - Harvey P. Dale, Nov 14 2011

From Amiram Eldar, Sep 06 2022: (Start)

Sum_{n>=0} 1/a(n) = 114905939/6480 - 5390*Pi^2/3.

Sum_{n>=0} (-1)^n/a(n) = 14336*log(2)/9 - 3577279/3240. (End)

Extensions

More terms from Harvey P. Dale, Nov 14 2011