OFFSET
1,1
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
FORMULA
From R. J. Mathar, Nov 18 2009: (Start)
a(n) = 3*a(n-2) - 3*a(n-4) + a(n-6).
G.f.: x*(2+3*x+6*x^2+x^3)/((1-x)^3*(1+x)^3).
a(2n+1) = A002939(n+1).
a(2n) = A014105(n). (End)
a(n) = lcm(n+1, binomial(n+1,2)). - Enrique Pérez Herrero, Mar 13 2012
From Ilya Gutkovskiy, Jul 08 2016: (Start)
E.g.f.: x*(x + 1)*sinh(x) + x*(x + 4)*cosh(x)/2.
a(n) = n*(n + 1)*(3 - (-1)^n)/4. (End)
Sum_{n>=1} 1/a(n) = 2 - log(2). - Amiram Eldar, Sep 11 2022
EXAMPLE
a(4) = 10 because 6/(5*4) = 3/10 has 10 in the denominator.
MATHEMATICA
Table[Denominator[(n+2)/(n+1)/n], {n, 60}]
PROG
(PARI) a(n) = denominator((n+2)/(n*(n+1))); \\ Michel Marcus, Jul 09 2016
(Magma) [Lcm(n+1, Binomial(n+1, 2)): n in [1..60]]; // Vincenzo Librandi, Mar 13 2018
CROSSREFS
KEYWORD
nonn,frac,easy
AUTHOR
Vladimir Joseph Stephan Orlovsky, Nov 17 2009
STATUS
approved