A168061 Denominator of (n+3) / ((n+2) * (n+1) * n).
3, 24, 10, 120, 105, 112, 252, 720, 165, 1320, 858, 728, 1365, 3360, 680, 4896, 2907, 2280, 3990, 9240, 1771, 12144, 6900, 5200, 8775, 19656, 3654, 24360, 13485, 9920, 16368, 35904, 6545, 42840, 23310, 16872, 27417, 59280, 10660, 68880, 37023, 26488, 42570
Offset: 1
Links
- G. C. Greubel, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,4,0,0,0,0,0,-6,0,0,0,0,0,4,0,0,0,0,0,-1).
Crossrefs
Cf. A060789.
Programs
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GAP
List([1..10^3],n->DenominatorRat((n+3)/(n+2)/(n+1)/n)); # Muniru A Asiru, Feb 04 2018
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Maple
seq(denom((n+3)/(n+2)/(n+1)/n), n=1..10^3); # Muniru A Asiru, Feb 04 2018
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Mathematica
Table[Denominator[(n+3)/(n+2)/(n+1)/n],{n,60}] LinearRecurrence[{0,0,0,0,0,4,0,0,0,0,0,-6,0,0,0,0,0,4,0,0,0,0,0,-1},{3,24,10,120,105,112,252,720,165,1320,858,728,1365,3360,680,4896,2907,2280,3990,9240,1771,12144,6900,5200},50] (* Harvey P. Dale, Apr 06 2017 *) -
PARI
vector(50, n, denominator(((n+3)/(n+2)/(n+1)/n))) \\ Colin Barker, Feb 04 2018
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PARI
Vec(x*(3 + 24*x + 10*x^2 + 120*x^3 + 105*x^4 + 112*x^5 + 240*x^6 + 624*x^7 + 125*x^8 + 840*x^9 + 438*x^10 + 280*x^11 + 375*x^12 + 624*x^13 + 80*x^14 + 336*x^15 + 105*x^16 + 40*x^17 + 30*x^18 + 24*x^19 + x^20) / ((1 - x)^4*(1 + x)^4*(1 - x + x^2)^4*(1 + x + x^2)^4) + O(x^60)) \\ Colin Barker, Feb 04 2018
Formula
a(n) = 4*a(n-6) -6*a(n-12) +4*a(n-18) -a(n-24) = A007531(n+2)/A089145(n). - R. J. Mathar, Nov 18 2009
G.f.: x*(3 + 24*x + 10*x^2 + 120*x^3 + 105*x^4 + 112*x^5 + 240*x^6 + 624*x^7 + 125*x^8 + 840*x^9 + 438*x^10 + 280*x^11 + 375*x^12 + 624*x^13 + 80*x^14 + 336*x^15 + 105*x^16 + 40*x^17 + 30*x^18 + 24*x^19 + x^20) / ((1 - x)^4*(1 + x)^4*(1 - x + x^2)^4*(1 + x + x^2)^4). - Colin Barker, Feb 04 2018
Comments