A105253 a(n) = binomial(n+6,n)*binomial(n+10,n).

1, 77, 1848, 24024, 210210, 1387386, 7399392, 33372768, 131405274, 462351890, 1479526048, 4365213216, 12004336344, 31040798712, 76018282560, 177375992640, 396324483555, 851617661895, 1766318113560, 3547314771000, 6917263803450, 13128684361650, 24304341297600

Offset: 0

Author

Zerinvary Lajos, Apr 14 2005

Keywords

• easy
• nonn

Examples

			a(0): C(0+6,0)*C(0+10,0) = C(6,0)*C(10,0) = 1*1 = 1;
a(10): C(10+6,10)*C(10+10,10) = C(16,10)*(20,10) = 8008*184756 = 1479526048.
		

Links

• T. D. Noe, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (17,-136,680,-2380,6188,-12376,19448,-24310,24310,-19448,12376,-6188,2380,-680,136,-17,1).

Crossrefs

Cf. A062264.

Programs

Magma

[Binomial(n+6,n)*Binomial(n+10,n): n in [0..30]]; // Vincenzo Librandi, Jul 31 2015

Mathematica

f[n_] := Binomial[n + 6, n]Binomial[n + 10, n]; Table[ f[n], {n, 0, 20}] (* Robert G. Wilson v, Apr 20 2005 *)

Python

A105253_list, m = [], [8008, -22022, 23023, -11297, 2563, -209] + [1]*11
for _ in range(10**2):
    A105253_list.append(m[-1])
    for i in range(16):
        m[i+1] += m[i] # Chai Wah Wu, Jan 24 2016

SageMath

def A105253(n): return binomial(n+6,n)*binomial(n+10,n)
print([A105253(n) for n in range(31)]) # G. C. Greubel, Mar 04 2025

Formula

G.f.: (1 + 60*x + 675*x^2 + 2400*x^3 + 3150*x^4 + 1513*x^5 + 210*x^6)/(1-x)^17. - Colin Barker, Jan 21 2013

From Amiram Eldar, Sep 01 2022: (Start)

Sum_{n>=0} 1/a(n) = 20020*Pi^2 - 1493768807/7560.

Sum_{n>=0} (-1)^n/a(n) = 131072*log(2)/21 - 100*Pi^2 - 88332653/26460. (End)

Extensions

More terms from Robert G. Wilson v, Apr 20 2005