Search: id:A119937
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%I A119937
%S A119937 3,32,5,135,27,7,3456,756,256,81,3500,800,300,125,44,172800,40500,16000,
%T A119937 7425,3456,1300,694575,165375,67375,33075,17199,8575,3375,6272000,
%U A119937 1509200,627200,318500,175616,98000,51200
%N A119937 Triangle of numbers related to the spectrum of the hydrogen (H) atom.
%C A119937 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 A119937 W. Lang: <a href="http://www-itp.physik.uni-karlsruhe.de/~wl/EISpub/A119937.text">
               First ten rows.</a>
%F A119937 a(m,n) = r(m,n)*LCM(seq(r(m,k),k = 1..m-1)) with r(m,n) = 1/n^2 - 1/m^2 
               = A120072(m,n)/A120073(m,n), m> = 2, n = 1..m-1.
%e A119937 [3]; [32,5]; [135,27,7]; [3456,756,256,81]; [3500,800,300,125,44]; ...
%Y A119937 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 A119937 The row sums give A119938.
%Y A119937 Sequence in context: A118913 A005042 A136582 this_sequence A114257 A107465 
               A119940
%Y A119937 Adjacent sequences: A119934 A119935 A119936 this_sequence A119938 A119939 
               A119940
%K A119937 nonn,easy,tabl
%O A119937 2,1
%A A119937 Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Jul 20 
               2006

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