OFFSET
0,1
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..680
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
From R. J. Mathar, Aug 15 2008: (Start)
O.g.f.: 12/(1-x)^5. (End)
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5); a(0)=12, a(1)=60, a(2)=180, a(3)=420, a(4)=840. - Harvey P. Dale, Jul 24 2011
From Amiram Eldar, Sep 04 2022: (Start)
Sum_{n>=0} 1/a(n) = 1/9.
Sum_{n>=0} (-1)^n/a(n) = 8*(3*log(2)-2)/9. (End)
EXAMPLE
n=0: C(1+0,1)*C(2+0,1)*C(4+0,2) = C(1,1)*C(2,1)*C(4,2) = 1*2*6 = 12;
n=10: C(1+10,1)*C(2+10,1)*C(4+10,2) = C(11,1)*C(12,1)*C(14,2) = 11*12*91 = 12012.
MATHEMATICA
Table[(n+1)(n+2)Binomial[4+n, 2], {n, 0, 30}] (* or *) LinearRecurrence[ {5, -10, 10, -5, 1}, {12, 60, 180, 420, 840}, 31] (* Harvey P. Dale, Jul 24 2011 *)
PROG
(Magma) [(n+1)*(n+2)*(n+3)*(n+4)/2: n in [0..40]]; // Vincenzo Librandi, Apr 28 2011
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Zerinvary Lajos, Dec 09 2005
STATUS
approved