A103604 a(n) = binomial(n+6,6) * binomial(n+10,6).

210, 3234, 25872, 144144, 630630, 2312310, 7399392, 21237216, 55747692, 135795660, 310390080, 671571264, 1385115732, 2738894004, 5216940960, 9610154400, 17178150990, 29881321470, 50707697040, 84126042000, 136704818250, 217946538810, 341398774080, 526116951360

Offset: 0

Author

Zerinvary Lajos, Apr 22 2005

Keywords

• nonn
• easy

Links

• T. D. Noe, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).

Crossrefs

Cf. A000579, A062264.

Programs

Magma

A103604:= func< n | Binomial(n+6,6)*Binomial(n+10,6) >;
[A103604(n): n in [0..30]]; // G. C. Greubel, Mar 05 2025

Mathematica

Table[Binomial[n+6,6]Binomial[n+10,6],{n,0,30}] (* or *) LinearRecurrence[ {13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1},{210,3234,25872, 144144,630630,2312310,7399392,21237216,55747692,135795660,310390080, 671571264,1385115732},30] (* Harvey P. Dale, Apr 18 2019 *)

PARI

a(n) = binomial(n+6,6)*binomial(n+10,6) \\ Colin Barker, Jul 01 2015

PARI

Vec(-42*(5*x^2+12*x+5)/(x-1)^13 + O(x^30)) \\ Colin Barker, Jul 01 2015

SageMath

def A103604(n): return binomial(n+6,6)*binomial(n+10,6)
print([A103604(n) for n in range(31)]) # G. C. Greubel, Mar 05 2025

Formula

G.f.: 42*(5+12*x+5*x^2) / (1-x)^13. - Colin Barker, Jul 01 2015

a(n) = A000579(n+6)*A000579(n+10). - Michel Marcus, Jul 01 2015

From Amiram Eldar, Sep 06 2022: (Start)

Sum_{n>=0} 1/a(n) = 60*Pi^2 - 10445899/17640.

Sum_{n>=0} (-1)^n/a(n) = 447173/2205 - 2048*log(2)/7. (End)