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A165441 Table T(k,n) read by antidiagonals: denominator of 1/min(n,k)^2 -1/max(n,k)^2.

%I A165441 #15 Feb 04 2020 14:58:02
%S A165441 1,4,4,9,1,9,16,36,36,16,25,16,1,16,25,36,100,144,144,100,36,49,9,225,
%T A165441 1,225,9,49,64,196,12,400,400,12,196,64,81,64,441,144,1,144,441,64,81,
%U A165441 100,324,576,784,900,900,784,576,324,100,121,25,81,64,1225,1,1225,64,81,25,121
%N A165441 Table T(k,n) read by antidiagonals: denominator of 1/min(n,k)^2 -1/max(n,k)^2.
%C A165441 A synopsis of the denominators of the transitions in the Rydberg-Ritz spectrum of hydrogenic atoms.
%H A165441 Alois P. Heinz, <a href="/A165441/b165441.txt">Table of n, a(n) for n = 1..1035</a>
%F A165441 T(n,k) = A165727(n,k).
%e A165441 .1,   4,   9,   16,   25,   36,   49,   64,   81, ... A000290
%e A165441 .4,   1,  36,   16,  100,    9,  196,   64,  324, ... A061038
%e A165441 .9,  36,   1,  144,  225,   12,  441,  576,   81, ... A061040
%e A165441 16,  16, 144,    1,  400,  144,  784,   64, 1296, ... A061042
%e A165441 25, 100, 225,  400,    1,  900, 1225, 1600, 2025, ... A061044
%e A165441 36,   9,  12,  144,  900,    1, 1764,  576,  324, ... A061046
%e A165441 49, 196, 441,  784, 1225, 1764,    1, 3136, 3969, ... A061048
%e A165441 64,  64, 576,   64, 1600,  576, 3136,    1, 5184, ... A061050
%e A165441 81, 324,  81, 1296, 2025,  324, 3969, 5184,    1, ...
%p A165441 T:= (k,n)-> denom(1/min (n,k)^2 -1/max (n, k)^2):
%p A165441 seq(seq(T(k, d-k), k=1..d-1), d=2..12);
%t A165441 T[n_, k_] := Denominator[1/Min[n, k]^2 - 1/Max[n, k]^2];
%t A165441 Table[T[n-k, k], {n, 2, 12}, {k, 1, n-1}] // Flatten (* _Jean-François Alcover_, Feb 04 2020 *)
%K A165441 nonn,tabl,frac,look,easy
%O A165441 1,2
%A A165441 _Paul Curtz_, Sep 19 2009
%E A165441 Edited by _R. J. Mathar_, Feb 27 2010, Mar 03 2010