OFFSET
1,1
COMMENTS
Numerator of ((n+3)/(n+2)/(n+1)/n) = A060789(n).
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).
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
MAPLE
seq(denom((n+3)/(n+2)/(n+1)/n), n=1..10^3); # Muniru A Asiru, Feb 04 2018
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 *)
PROG
(PARI) vector(50, n, denominator(((n+3)/(n+2)/(n+1)/n))) \\ Colin Barker, Feb 04 2018
(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
(GAP) List([1..10^3], n->DenominatorRat((n+3)/(n+2)/(n+1)/n)); # Muniru A Asiru, Feb 04 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vladimir Joseph Stephan Orlovsky, Nov 17 2009
STATUS
approved