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A120074 Row sums of triangle A120072 (numerator triangle for H atom spectrum).

%I A120074 #12 Apr 25 2023 06:18:39
%S A120074 3,13,25,70,54,203,197,340,303,825,445,1378,892,1221,1565,3128,1545,
%T A120074 4389,2427,3592,3688,7843,3589,8420,6191,9097,7135,15834,5774,19375,
%U A120074 12493,14814,14147,19647,12264,33078
%N A120074 Row sums of triangle A120072 (numerator triangle for H atom spectrum).
%H A120074 G. C. Greubel, <a href="/A120074/b120074.txt">Table of n, a(n) for n = 2..1000</a>
%F A120074 a(n) = Sum_{k=1..n-1} A120072(n,k) for n >= 2.
%t A120074 Table[Sum[1/n^2 - 1/m^2 //Numerator, {n,m-1}], {m,2,40}]  (* _Jean-François Alcover_, Sep 16 2013 *)
%o A120074 (Magma)
%o A120074 A120072:= func< n,k | Numerator(1/k^2 - 1/n^2) >;
%o A120074 [(&+[A120072(n,k): k in [1..n-1]]): n in [2..50]]; // _G. C. Greubel_, Apr 24 2023
%o A120074 (SageMath)
%o A120074 def A120072(n,k): return numerator(1/k^2 - 1/n^2)
%o A120074 [sum(A120072(n,k) for k in range(1,n)) for n in range(2,51)] # _G. C. Greubel_, Apr 24 2023
%Y A120074 Cf. A120070, A120072, A120073, A120075, A120076, A120077.
%K A120074 nonn,easy
%O A120074 2,1
%A A120074 _Wolfdieter Lang_, Jul 20 2006