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A120075 Row sums of triangle A120073 (denominator triangle for H atom spectrum).

%I A120075 #7 Apr 25 2023 06:18:50
%S A120075 4,45,176,750,1101,4459,6080,13284,16350,46585,33954,109850,92463,
%T A120075 142705,198400,432344,255096,761349,500355,824866,925529,2007555,
%U A120075 1044616,2612500,2158130,3301641,2848741
%N A120075 Row sums of triangle A120073 (denominator triangle for H atom spectrum).
%H A120075 G. C. Greubel, <a href="/A120075/b120075.txt">Table of n, a(n) for n = 2..1000</a>
%F A120075 a(n) = Sum_{k=1..n-1} A120073(n,k), for n >= 2.
%t A120075 A120075[n_]:= Sum[Denominator[1/k^2 -1/n^2], {k,n-1}];
%t A120075 Table[A120075[n], {n,2,50}] (* _G. C. Greubel_, Apr 24 2023 *)
%o A120075 (Magma)
%o A120075 A120073:= func< n,k | Denominator(1/k^2 - 1/n^2) >;
%o A120075 [(&+[A120073(n,k): k in [1..n-1]]): n in [2..50]]; // _G. C. Greubel_, Apr 24 2023
%o A120075 (SageMath)
%o A120075 def A120073(n,k): return denominator(1/k^2 - 1/n^2)
%o A120075 [sum(A120073(n,k) for k in range(1,n)) for n in range(2,51)] # _G. C. Greubel_, Apr 24 2023
%Y A120075 Cf. A120070, A120072, A120073, A120074, A120076, A120077.
%K A120075 nonn,easy
%O A120075 2,1
%A A120075 _Wolfdieter Lang_, Jul 20 2006