A168061 - OEIS

%I #18 Feb 04 2018 12:36:46

%S 3,24,10,120,105,112,252,720,165,1320,858,728,1365,3360,680,4896,2907,

%T 2280,3990,9240,1771,12144,6900,5200,8775,19656,3654,24360,13485,9920,

%U 16368,35904,6545,42840,23310,16872,27417,59280,10660,68880,37023,26488,42570

%N Denominator of (n+3) / ((n+2) * (n+1) * n).

%C Numerator of ((n+3)/(n+2)/(n+1)/n) = A060789(n).

%H G. C. Greubel, <a href="/A168061/b168061.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_24">Index entries for linear recurrences with constant coefficients</a>, 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).

%F 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

%F 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

%p seq(denom((n+3)/(n+2)/(n+1)/n), n=1..10^3); # _Muniru A Asiru_, Feb 04 2018

%t Table[Denominator[(n+3)/(n+2)/(n+1)/n],{n,60}]

%t 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 *)

%o (PARI) vector(50, n, denominator(((n+3)/(n+2)/(n+1)/n))) \\ _Colin Barker_, Feb 04 2018

%o (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

%o (GAP) List([1..10^3],n->DenominatorRat((n+3)/(n+2)/(n+1)/n)); # _Muniru A Asiru_, Feb 04 2018

%Y Cf. A060789.

%K nonn,easy

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Nov 17 2009