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A118411 Numerator of sum of reciprocals of first n pentatope numbers A000332. 4
1, 6, 19, 136, 83, 119, 656, 73, 190, 121, 1816, 559, 679, 815, 3872, 1139, 886, 513, 2360, 2023, 2299, 2599, 11696, 3275, 7306, 1353, 5992, 1653, 5455, 5983, 26176, 7139, 15538, 8435, 12184, 3293, 3553, 11479, 49360 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Denominators are A118412. Fractions are: 1/1, 6/5, 19/15, 136/105, 83/63, 119/90, 656/495, 73/55, 190/143, 121/91, 1816/1365, 559/420, 679/510, 815/612, 3872/2907, 1139/855, 886/665, 513/385, 2360/1771, 2023/1518, 2299/1725, 2599/1950, 11696/8775, 3275/2457, 7306/5481, 1353/1015, 5992/4495, 1653/1240, 5455/4092, 5983/4488, 26176/19635, 7139/5355, 15538/11655, 8435/6327, 12184/9139, 3293/2470, 3553/2665, 11479/8610, 49360/37023. The denominator of sum of reciprocals of first n triangular numbers is A026741. The denominator of sum of reciprocals of first n tetrahedral numbers is A118392.

LINKS

Table of n, a(n) for n=1..39.

FORMULA

A118411(n)/A118412(n) = SUM[i=1..n] (1/A000332(n)). A118411(n)/A118412(n) = SUM[i=1..n] (1/C(n+2,4)). A118411(n)/A118412(n) = SUM[i=1..n] (1/(n*(n+1)*(n+2)*(n+3)/24)).

EXAMPLE

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

a(2) = 6 = numerator of 6/5 = 1/1 + 1/5.

a(3) = 19 = numerator of 19/15 = 1/1 + 1/5 + 1/15.

a(4) = 136 = numerator of 136/105 = 1/1 + 1/5 + 1/15 + 1/35.

a(5) = 55 = numerator of 55/42 = 1/1 + 1/5 + 1/15 + 1/35 + 1/70.

a(10) = 190 = numerator of 190/143 = 1/1 + 1/5 + 1/15 + 1/35 + 1/70 + 1/126 + 1/210 + 1/330 + 1/495 + 1/715.

a(20) = 2360 = numerator of 2360/1771 = 1/1 + 1/5 + 1/15 + 1/35 + 1/70 + 1/126 + 1/210 + 1/330 + 1/495 + 1/715 + 1/1001 + 1/1365 + 1/1820 + 1/2380 + 1/3060 + 1/3876 + 1/4845 + 1/5985 + 1/7315 + 1/8855.

PROG

(Pari) s=0; for(i=4, 50, s+=1/binomial(i, 4); print(numerator(s))) /* Phil Carmody, Mar 27 2012 */

CROSSREFS

Cf. A000332, A022998, A026741, A118391, A118391, A118412.

Sequence in context: A097899 A223505 A054236 * A091876 A041066 A060748

Adjacent sequences:  A118408 A118409 A118410 * A118412 A118413 A118414

KEYWORD

easy,frac,nonn

AUTHOR

Jonathan Vos Post, Apr 27 2006

STATUS

approved

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Last modified July 31 21:49 EDT 2014. Contains 245088 sequences.