%I A120072
%S A120072 3,8,5,15,3,7,24,21,16,9,35,2,1,5,11,48,45,40,33,24,13,63,15,55,3,39,7,
%T A120072 15,80,77,8,65,56,5,32,17,99,6,91,21,3,4,51,9,19,120,117,112,105,96,85,
%U A120072 72,57,40,21,143,35,5,1
%N A120072 Numerator triangle for hydrogen spectrum rationals.
%C A120072 Frequencies or energies of the spectral lines of the hydrogen (H) atom 
               are given, according to quantum theory, by r(m,n)*3.287*PHz (1 Peta 
               Hertz= 10^15 s^{-1}) or r(m,n)*13.599 eV (electron Volts), respectively. 
               The wave lengths are lambda(m,n) = (1/r(m,n))* 91.196 nm (all decimals 
               rounded). See the W. Lang link for more details.
%C A120072 The spectral series for n=1,2,...,5, m>=n+1, are named after Lyman, Balmer, 
               Paschen, Brackett, Pfund, respectively.
%C A120072 The corresponding denominator triangle is A120073.
%C A120072 The rationals are r(m,n):= A120072(m,n)/A120073(m,n) = A120070(m,n)/(m^2*n^2)= 
               1/ n^2 - 1/m^2 and they are given in lowest terms.
%H A120072 W. Lang: <a href="http://www-itp.physik.uni-karlsruhe.de/~wl/EISpub/A120072.text">
               First ten rows, rationals and more.</a>
%F A120072 a(m,n)=numerator(r(m,n)) with r(m,n):=1/n^2 - 1/m^2, m>=2, n=1..m-1.
%F A120072 The g.f.s for the columns n=1,..,10 of triangle r(m,n):=A120072(m,n)/
               A120073(m,n), m>=2, 1<= n<=m-1, are given in the W. Lang link.
%Y A120072 Row sums give A120074. Row sums of r(m, n) triangle give A120076(m)/A120077(m), 
               m>=2.
%Y A120072 Cf. A126252.
%Y A120072 Sequence in context: A058055 A078356 A050093 this_sequence A166492 A143813 
               A120070
%Y A120072 Adjacent sequences: A120069 A120070 A120071 this_sequence A120073 A120074 
               A120075
%K A120072 nonn,easy,tabl,frac
%O A120072 2,1
%A A120072 Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Jul 20 
               2006