OFFSET
1,1
COMMENTS
Also denominator of h(n+2) - h(n-1), where h(n) is the n-th harmonic number Sum_{k=1..n} 1/k, the numerator is A188386. - Reinhard Zumkeller, Jul 04 2012
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (0,4,0,-6,0,4,0,-1).
FORMULA
a(n) = n*(n+1)*(n+2)*[3-(-1)^n]/4.
From Reinhard Zumkeller, Jul 04 2012: (Start)
a(n) = 6 * A067046(n).
From Amiram Eldar, Sep 29 2022: (Start)
Sum_{n>=1} 1/a(n) = 1 - log(2) (A244009).
Sum_{n>=1} (-1)^(n+1)/a(n) = 3*log(2) - 2. (End)
MATHEMATICA
LCM@@@Partition[Range[50], 3, 1] (* or *) LinearRecurrence[{0, 4, 0, -6, 0, 4, 0, -1}, {6, 12, 60, 60, 210, 168, 504, 360}, 50] (* Harvey P. Dale, Jun 29 2019 *)
PROG
(Haskell)
a033931 n = lcm n (lcm (n + 1) (n + 2)) -- Reinhard Zumkeller, Jul 04 2012
(Magma) [Numerator((n^3-n)/(n^2+1)): n in [2..50]]; // Vincenzo Librandi, Aug 19 2014
(PARI) a(n) = lcm(n^2+n, n+2) \\ Charles R Greathouse IV, Sep 30 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved