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

1,2

Comments

Numerators are A118391.

Links

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

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

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A000292, A022998, A026741, A118391.

Sequence in context: A081852 A050017 A125514 * A263964 A180855 A213822

Adjacent sequences: A118389 A118390 A118391 * A118393 A118394 A118395

Keyword

easy,frac,nonn

Author

Jonathan Vos Post, Apr 27 2006

Extensions

More terms from Harvey P. Dale, Jun 07 2018

Status

approved