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%I #11 Aug 28 2019 17:14:01
%S 3,32,5,135,27,7,3456,756,256,81,3500,800,300,125,44,172800,40500,
%T 16000,7425,3456,1300,694575,165375,67375,33075,17199,8575,3375,
%U 6272000,1509200,627200,318500,175616,98000,51200
%N Triangle of numbers related to the spectrum of the hydrogen (H) atom.
%C 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.
%H W. Lang: <a href="/A119937/a119937.txt">First ten rows.</a>
%F 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.
%e [3]; [32,5]; [135,27,7]; [3456,756,256,81]; [3500,800,300,125,44]; ...
%Y 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.
%Y The row sums give A119938.
%K nonn,easy,tabl
%O 2,1
%A _Wolfdieter Lang_, Jul 20 2006
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