A118411 Numerator of sum of reciprocals of first n pentatope numbers A000332.

1, 6, 19, 136, 55, 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, 13243, 28378, 15179, 64856, 5765, 6141

Offset

1,2

Comments

Denominators are A118412. 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

Paolo Xausa, Table of n, a(n) for n = 1..10000

Formula

A118411(n)/A118412(n) = Sum_{i=1..n} 1/A000332(i+3).

A118411(n)/A118412(n) = Sum_{i=1..n} 1/C(i+3,4).

A118411(n)/A118412(n) = Sum_{i=1..n} 24/(i*(i+1)*(i+2)*(i+3)).

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.

Mathematica

Numerator[Accumulate[1/Binomial[Range[4, 50], 4]]] (* Paolo Xausa, Sep 27 2025 *)

Prog

(PARI) s=0; for(i=4, 50, s+=1/binomial(i, 4); print1(numerator(s)", ")) /* Phil Carmody, Mar 27 2012 */

Crossrefs

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

Sequence in context: A223505 A395798 A054236 * A091876 A041066 A060748

Adjacent sequences: A118408 A118409 A118410 * A118412 A118413 A118414

Keyword

easy,frac,nonn

Author

Jonathan Vos Post, Apr 27 2006

Extensions

a(5) = 55 added and more terms from Jason Yuen, Sep 27 2025

Status

approved