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

4, 45, 176, 750, 1101, 4459, 6080, 13284, 16350, 46585, 33954, 109850, 92463, 142705, 198400, 432344, 255096, 761349, 500355, 824866, 925529, 2007555, 1044616, 2612500, 2158130, 3301641, 2848741

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, A120074, A120076, A120077.

Programs

Magma

A120073:= func< n,k | Denominator(1/k^2 - 1/n^2) >;
[(&+[A120073(n,k): k in [1..n-1]]): n in [2..50]]; // G. C. Greubel, Apr 24 2023

Mathematica

A120075[n_]:= Sum[Denominator[1/k^2 -1/n^2], {k,n-1}];
Table[A120075[n], {n,2,50}] (* G. C. Greubel, Apr 24 2023 *)

SageMath

def A120073(n,k): return denominator(1/k^2 - 1/n^2)
[sum(A120073(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} A120073(n,k), for n >= 2.