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A165727 Table T(k,n) read by antidiagonals: denominator of 1/min(n,k)^2 -1/max(n,k)^2 with T(0,n) = T(k,0) = 0.

%I A165727 #13 Mar 30 2012 18:52:03
%S A165727 0,0,0,0,1,0,0,4,4,0,0,9,1,9,0,0,16,36,36,16,0,0,25,16,1,16,25,0,0,36,
%T A165727 100,144,144,100,36,0,0,49,9,225,1,225,9,49,0,0,64,196,12,400,400,12,
%U A165727 196,64,0,0,81,64,441,144,1,144,441,64,81,0,0,100,324,576,784,900,900,784,576,324,100,0
%N A165727 Table T(k,n) read by antidiagonals: denominator of 1/min(n,k)^2 -1/max(n,k)^2 with T(0,n) = T(k,0) = 0.
%C A165727 A synopsis of the denominators of the transitions in the Rydberg-Ritz spectrum of hydrogenic atoms.
%H A165727 Alois P. Heinz, <a href="/A165727/b165727.txt">Table of n, a(n) for n = 0..1034</a>
%e A165727 0,  0,   0,   0,    0,    0,    0,    0,    0,    0, ... A000004
%e A165727 0,  1,   4,   9,   16,   25,   36,   49,   64,   81, ... A000290
%e A165727 0,  4,   1,  36,   16,  100,    9,  196,   64,  324, ... A061038
%e A165727 0,  9,  36,   1,  144,  225,   12,  441,  576,   81, ... A061040
%e A165727 0, 16,  16, 144,    1,  400,  144,  784,   64, 1296, ... A061042
%e A165727 0, 25, 100, 225,  400,    1,  900, 1225, 1600, 2025, ... A061044
%e A165727 0, 36,   9,  12,  144,  900,    1, 1764,  576,  324, ... A061046
%e A165727 0, 49, 196, 441,  784, 1225, 1764,    1, 3136, 3969, ... A061048
%e A165727 0, 64,  64, 576,   64, 1600,  576, 3136,    1, 5184, ... A061050
%e A165727 0, 81, 324,  81, 1296, 2025,  324, 3969, 5184,    1, ...
%p A165727 T:= (k,n)-> `if` (n=0 or k=0, 0, denom (1/min (n,k)^2 -1/max (n, k)^2)):
%p A165727 seq (seq (T (k, d-k), k=0..d), d=0..11);
%Y A165727 Cf. A165441 (top row and left column removed)
%K A165727 nonn,tabl,frac,easy
%O A165727 0,8
%A A165727 _Paul Curtz_, Sep 25 2009
%E A165727 Edited by _R. J. Mathar_, Feb 27 2010, Mar 03 2010