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A118392
Denominator of sum of reciprocals of first n tetrahedral numbers A000292.
5
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
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
KEYWORD
easy,frac,nonn
AUTHOR
Jonathan Vos Post, Apr 27 2006
EXTENSIONS
More terms from Harvey P. Dale, Jun 07 2018
STATUS
approved