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

3, 13, 25, 70, 54, 203, 197, 340, 303, 825, 445, 1378, 892, 1221, 1565, 3128, 1545, 4389, 2427, 3592, 3688, 7843, 3589, 8420, 6191, 9097, 7135, 15834, 5774, 19375, 12493, 14814, 14147, 19647, 12264, 33078

Offset: 2

Author

Wolfdieter Lang, Jul 20 2006

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 2..1000

Crossrefs

Cf. A120070, A120072, A120073, A120075, A120076, A120077.

Programs

Magma

A120072:= func< n,k | Numerator(1/k^2 - 1/n^2) >;
[(&+[A120072(n,k): k in [1..n-1]]): n in [2..50]]; // G. C. Greubel, Apr 24 2023

Mathematica

Table[Sum[1/n^2 - 1/m^2 //Numerator, {n,m-1}], {m,2,40}]  (* Jean-François Alcover, Sep 16 2013 *)

SageMath

def A120072(n,k): return numerator(1/k^2 - 1/n^2)
[sum(A120072(n,k) for k in range(1,n)) for n in range(2,51)] # G. C. Greubel, Apr 24 2023

Formula

a(n) = Sum_{k=1..n-1} A120072(n,k) for n >= 2.