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A118391 Numerator of sum of reciprocals of first n tetrahedral numbers A000292. 7
1, 5, 27, 7, 10, 81, 35, 22, 81, 65, 77, 135, 52, 119, 405, 76, 85, 567, 209, 115, 378, 275, 299, 486, 175, 377, 1215, 217, 232, 1485, 527, 280, 891, 629, 665, 1053, 370, 779, 2457, 430, 451, 2835, 989, 517, 1620, 1127, 1175, 1836, 637, 1325, 4131, 715, 742 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Denominators are A118392. 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. The numerator of sum of reciprocals of first n triangular numbers is A022998.

2n+3 divides a(2n). 2n-1 divides a(2n-1). p divides a(p) for prime p>2. The only primes in a(n) are a(2) = 5 and a(4) = 7. - Alexander Adamchuk, May 08 2007

LINKS

Table of n, a(n) for n=1..53.

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] (1/(n*(n+1)*(n+2)/6)).

a(n) = Numerator[ 3n(n+3) / (2(n+1)(n+2)) ]. - Alexander Adamchuk, May 08 2007

EXAMPLE

a(1) = 1 = numerator of 1/1.

a(2) = 5 = numerator of 5/4 = 1/1 + 1/4.

a(3) = 27 = numerator of 27/20 = 1/1 + 1/4 + 1/10.

a(4) = 7 = numerator of 7/5 = 1/1 + 1/4 + 1/10 + 1/20.

a(5) = 10 = numerator of 10/7 = 1/1 + 1/4 + 1/10 + 1/20 + 1/35.

a(20) = 115 = numerator 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.

MATHEMATICA

Table[ Numerator[ 3n(n+3) / (2(n+1)(n+2)) ], {n, 1, 100} ] - Alexander Adamchuk, May 08 2007

PROG

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

CROSSREFS

Cf. A000292, A022998, A118392.

Sequence in context: A064489 A081089 A180928 * A196085 A097088 A196009

Adjacent sequences:  A118388 A118389 A118390 * A118392 A118393 A118394

KEYWORD

easy,frac,nonn

AUTHOR

Jonathan Vos Post, Apr 27 2006

EXTENSIONS

More terms from Alexander Adamchuk, May 08 2007

STATUS

approved

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Last modified June 4 02:04 EDT 2020. Contains 334812 sequences. (Running on oeis4.)