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A045896 Denominator of n/((n+1)*(n+2)) = A026741/A045896. 15
1, 6, 6, 20, 15, 42, 28, 72, 45, 110, 66, 156, 91, 210, 120, 272, 153, 342, 190, 420, 231, 506, 276, 600, 325, 702, 378, 812, 435, 930, 496, 1056, 561, 1190, 630, 1332, 703, 1482, 780, 1640, 861, 1806, 946, 1980, 1035, 2162, 1128, 2352, 1225, 2550, 1326 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Also period length divided by 2 of pairs (a,b), where a has period 2*n-2 and b has period n.
From Paul Curtz, Apr 17 2014: (Start)
Difference table of A026741/A045896:
0, 1/6, 1/6, 3/20, 2/15, 5/42, ...
1/6, 0, -1/60, -1/60, -1/70, -1/84, ... = 1/6, -A051712/A051713
-1/6, -1/60, 0, 1/420, 1/420, 1/504, ...
3/20, 1/60, 1/420, 0, -1/2520, -1/2520, ...
-2/15, -1/70, -1/420, -1/2520, 0, 1/13860, ...
5/42, 1/84, 1/504, 1/2520, -1/13860, 0, ...
Autosequence of the first kind. The main diagonal is A000004. The first two upper diagonals are equal. Their denominators are A000911. (End)
LINKS
Ralf W. Grosse-Kunstleve, Origin of EIS sequences A045895 & A045896. [Wayback Machine copy]
Masanobu Kaneko, The Akiyama-Tanigawa algorithm for Bernoulli numbers, J. Integer Sequences, 3 (2000), Article 00.2.9.
FORMULA
G.f.: (2*x^3+3*x^2+6*x+1)/(1-x^2)^3.
a(n) = (n+1)*(n+2) if n odd; or (n+1)*(n+2)/2 if n even = (n+1)*(n+2)*(3-(-1)^n)/4. - C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 16 2004
a(2*n) = A000384(n+1); a(2*n+1) = A026741(n+1). - Reinhard Zumkeller, Dec 12 2011
Sum_{n>=0} 1/a(n) = 1 + log(2). - Amiram Eldar, Sep 11 2022
From Amiram Eldar, Sep 14 2022: (Start)
a(n) = lcm(2*n+2, n+2)/2.
a(n) = A045895(n+2)/2. (End)
MAPLE
seq((n+1)*(n+2)*(3-(-1)^n)/4, n=0..20); # C. Ronaldo
with(combinat): seq(lcm(n+1, binomial(n+2, n)), n=0..50); # Zerinvary Lajos, Apr 20 2008
MATHEMATICA
Table[LCM[2*n + 2, n + 2]/2, {n, 0, 40}] (* corrected by Amiram Eldar, Sep 14 2022 *)
Denominator[#[[1]]/(#[[2]]#[[3]])&/@Partition[Range[0, 60], 3, 1]] (* Harvey P. Dale, Aug 15 2013 *)
PROG
(Haskell)
import Data.Ratio ((%), denominator)
a045896 n = denominator $ n % ((n + 1) * (n + 2))
-- Reinhard Zumkeller, Dec 12 2011
(PARI) Vec((2*x^3+3*x^2+6*x+1)/(1-x^2)^3+O(x^99)) \\ Charles R Greathouse IV, Mar 23 2016
CROSSREFS
Factor of A160466.
Sequence in context: A255468 A246037 A351832 * A309122 A115046 A004983
KEYWORD
nonn,easy,frac,nice
AUTHOR
STATUS
approved

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Last modified March 19 07:21 EDT 2024. Contains 370955 sequences. (Running on oeis4.)