A118392 Denominator of sum of reciprocals of first n tetrahedral numbers A000292.

1, 4, 20, 5, 7, 56, 24, 15, 55, 44, 52, 91, 35, 80, 272, 51, 57, 380, 140, 77, 253, 184, 200, 325, 117, 252, 812, 145, 155, 992, 352, 187, 595, 420, 444, 703, 247, 520, 1640, 287, 301, 1892, 660, 345, 1081, 752, 784, 1225, 425, 884, 2756, 477, 495, 3080

Offset: 1

Author

Jonathan Vos Post, Apr 27 2006

Keywords

• easy
• frac
• nonn

Comments

Numerators are A118391.

Examples

			a(1) = 1 = denominator of 1/1.
a(2) = 4 = denominator of 5/4 = 1/1 + 1/4.
a(3) = 20 = denominator of 27/20 = 1/1 + 1/4 + 1/10.
a(4) = 5 = denominator of 7/5 = 1/1 + 1/4 + 1/10 + 1/20.
a(5) = 7 = denominator of 10/7 = 1/1 + 1/4 + 1/10 + 1/20 + 1/35.
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.
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.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000292, A022998, A026741, A118391.

Programs

Magma

[Denominator(3*n*(n+3)/(2*(n+1)*(n+2))): n in [1..60]]; // G. C. Greubel, Feb 18 2021

Maple

A118392:= n -> denom(3*n*(n+3)/(2*(n+1)*(n+2)));
seq(A118392(n), n = 1..60); # G. C. Greubel, Feb 18 2021

Mathematica

Accumulate[1/Binomial[Range[70]+2,3]]//Denominator (* Harvey P. Dale, Jun 07 2018 *)

PARI

s=0;for(i=3,50,s+=1/binomial(i,3);print(denominator(s))) /* Phil Carmody, Mar 27 2012 */

Sage

[denominator(3*n*(n+3)/(2*(n+1)*(n+2))) for n in (1..60)] # G. C. Greubel, Feb 18 2021

Formula

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

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

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

a(n) = denominator( 3*n*(n+3)/(2*(n+1)*(n+2)) ). - G. C. Greubel, Feb 18 2021

Extensions

More terms from Harvey P. Dale, Jun 07 2018