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

2,1

Links

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

Formula

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

Mathematica

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

Prog

(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
(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

Crossrefs

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

Sequence in context: A146371 A146379 A056714 * A056706 A052454 A330718

Adjacent sequences: A120071 A120072 A120073 * A120075 A120076 A120077

Keyword

nonn,easy

Author

Wolfdieter Lang, Jul 20 2006

Status

approved