A119937 Triangle of numbers related to the spectrum of the hydrogen (H) atom.

3, 32, 5, 135, 27, 7, 3456, 756, 256, 81, 3500, 800, 300, 125, 44, 172800, 40500, 16000, 7425, 3456, 1300, 694575, 165375, 67375, 33075, 17199, 8575, 3375, 6272000, 1509200, 627200, 318500, 175616, 98000, 51200

Offset

2,1

Comments

The rational number triangle r(m,n):=A120072(m,n)/A120073(m,n), used to compute the spectral series of the hydrogen atom, is mapped to this nonnegative number triangle by multiplying the least common multiples (LCM) for each row m.

Links

Table of n, a(n) for n=2..36.

W. Lang: First ten rows.

Formula

a(m,n) = r(m,n)*lcm_{k=1..m-1} seq(r(m,k)) with r(m,n) = 1/n^2 - 1/m^2 = A120072(m,n)/A120073(m,n), m >= 2, n = 1..m-1.

Example

[3]; [32,5]; [135,27,7]; [3456,756,256,81]; [3500,800,300,125,44]; ...

Crossrefs

The LCM sequence which has been used here is [4, 36, 144, 3600, 3600, 176400, 705600, 6350400, 6350400, 768398400, ...] = A051418(m) = (A003418(m))^2 = (2*A025555(m-1))^2, m >= 2.

The row sums give A119938.

Sequence in context: A356516 A173649 A210648 * A254312 A304048 A324223

Adjacent sequences: A119934 A119935 A119936 * A119938 A119939 A119940

Keyword

nonn,easy,tabl

Author

Wolfdieter Lang, Jul 20 2006

Status

approved