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A230328 Denominator of n(n+3)/(4(n+1)(n+2)) = sum(k=1..n, 1/(k(k+1)(k+2)) ). 5
1, 6, 24, 40, 30, 21, 112, 144, 45, 110, 264, 312, 182, 105, 480, 544, 153, 342, 760, 840, 462, 253, 1104, 1200, 325, 702, 1512, 1624, 870, 465, 1984, 2112, 561, 1190, 2520, 2664, 1406, 741, 3120, 3280, 861, 1806, 3784, 3960, 2070, 1081, 4512 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
Jean-François Alcover, Table of n, a(n) for n = 0..1000
Wikipedia, Quasi-polynomial
FORMULA
G.f.: -(x^18 +3*x^17 +12*x^16 -6*x^15 +9*x^14 +91*x^12 -138*x^11 +183*x^10 -134*x^9 +183*x^8 -138*x^7 +91*x^6 +9*x^4 -6*x^3 +12*x^2 +3*x +1) / ((x -1)^3*(x^2 +1)^3*(x^4 +1)^3). - Colin Barker, Oct 09 2014 [Confirmed by Peter Bala, Feb 27 2019]
From Peter Bala, Feb 26 2019: (Start)
a(n) = 4*(n + 1)*(n + 2)/gcd(4*(n + 1)*(n + 2), n*(n + 3)).
a(n ) is quasi-polynomial in n; a(n) = (n + 1)*(n + 2)/2 when n = 0, 5 (mod 8); a(n) = (n + 1)*(n + 2) when n = 1, 4 (mod 8); a(n) = 2*(n + 1)*(n + 2) when n = 2, 3, 6, 7 (mod 8).
(End)
MAPLE
seq( 4*(n + 1)*(n + 2)/igcd(4*(n + 1)*(n + 2), n*(n + 3)), n = 0..100); - Peter Bala, Feb 26 2019
MATHEMATICA
Table[Denominator[n*(n+3)/(4*(n+1)*(n+2))], {n, 0, 100}]
PROG
(PARI) vector(100, n, denominator((n-1)*(n+2)/(4*n*(n+1)))) \\ Colin Barker, Oct 09 2014
CROSSREFS
Cf. A125650 (numerators).
Sequence in context: A247271 A065743 A225363 * A082195 A273788 A063961
KEYWORD
nonn,frac,easy
AUTHOR
STATUS
approved

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Last modified April 14 07:36 EDT 2024. Contains 371655 sequences. (Running on oeis4.)