A118392 - OEIS

%I #19 Feb 19 2021 09:45:58

%S 1,4,20,5,7,56,24,15,55,44,52,91,35,80,272,51,57,380,140,77,253,184,

%T 200,325,117,252,812,145,155,992,352,187,595,420,444,703,247,520,1640,

%U 287,301,1892,660,345,1081,752,784,1225,425,884,2756,477,495,3080

%N Denominator of sum of reciprocals of first n tetrahedral numbers A000292.

%C Numerators are A118391.

%H G. C. Greubel, <a href="/A118392/b118392.txt">Table of n, a(n) for n = 1..1000</a>

%F A118391(n)/A118392(n) = Sum_{i=1..n} 1/A000292(n).

%F A118391(n)/A118392(n) = Sum_{i=1..n} 1/C(n+2,3).

%F A118391(n)/A118392(n) = Sum_{i=1..n} 6/(n*(n+1)*(n+2)).

%F a(n) = denominator( 3*n*(n+3)/(2*(n+1)*(n+2)) ). - _G. C. Greubel_, Feb 18 2021

%e a(1) = 1 = denominator of 1/1.

%e a(2) = 4 = denominator of 5/4 = 1/1 + 1/4.

%e a(3) = 20 = denominator of 27/20 = 1/1 + 1/4 + 1/10.

%e a(4) = 5 = denominator of 7/5 = 1/1 + 1/4 + 1/10 + 1/20.

%e a(5) = 7 = denominator of 10/7 = 1/1 + 1/4 + 1/10 + 1/20 + 1/35.

%e a(20) = 77 = denominator of 115/77 = 1/1 + 1/4 + 1/10 + 1/20 + 1/35 + 1/56 + 1/84 + 1/120 + 1/165 + 1/220 + 1/286 + 1/364 + 1/455 + 1/560 + 1/680 + 1/816 + 1/969 + 1/1140 + 1/1330 + 1/1540.

%e Fractions are: 1/1, 5/4, 27/20, 7/5, 10/7, 81/56, 35/24, 22/15, 81/55, 65/44, 77/52, 135/91, 52/35, 119/80, 405/272, 76/51, 85/57, 567/380, 209/140, 115/77, 378/253, 275/184, 299/200, 486/325, 175/117, 377/252, 1215/812, 217/145, 232/155, 1485/992.

%p A118392:= n -> denom(3*n*(n+3)/(2*(n+1)*(n+2)));

%p seq(A118392(n), n = 1..60); # _G. C. Greubel_, Feb 18 2021

%t Accumulate[1/Binomial[Range[70]+2,3]]//Denominator (* _Harvey P. Dale_, Jun 07 2018 *)

%o (PARI) s=0;for(i=3,50,s+=1/binomial(i,3);print(denominator(s))) /* _Phil Carmody_, Mar 27 2012 */

%o (Sage) [denominator(3*n*(n+3)/(2*(n+1)*(n+2))) for n in (1..60)] # _G. C. Greubel_, Feb 18 2021

%o (Magma) [Denominator(3*n*(n+3)/(2*(n+1)*(n+2))): n in [1..60]]; // _G. C. Greubel_, Feb 18 2021

%Y Cf. A000292, A022998, A026741, A118391.

%K easy,frac,nonn

%O 1,2

%A _Jonathan Vos Post_, Apr 27 2006

%E More terms from _Harvey P. Dale_, Jun 07 2018