A120107 a(n) = Sum_{k=0..floor(n/2)} lcm(1,...,2*(n-k)+2)/lcm(1,...,2*k+2).

1, 6, 31, 425, 1331, 14084, 182533, 390855, 6192220, 117429752, 136000866, 2700408581, 13835919839, 42477252404, 1171690228133, 72397239805085, 84274330442804, 86644937313210, 2686078920033439, 3119346038772923

Offset: 0

Author

Paul Barry, Jun 09 2006

Keywords

• easy
• nonn

Comments

Diagonal sums of number triangle A120101.

Links

• Muniru A Asiru, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A120101, A120105, A120106.

Programs

GAP

List([0..20],n->Sum([0..Int(n/2)],k->Lcm(List([1..2*(n-k)+2],i->i))/Lcm(List([1..2*k+2],i->i)))); # Muniru A Asiru, Mar 03 2019

Magma

A120105:= func< n,k | Lcm([1..2*n+2])/Lcm([1..2*k+2]) >;
[(&+[A120105(n-k,k): k in [0..Floor(n/2)]]): n in [0..50]]; // G. C. Greubel, May 04 2023

Mathematica

A120105[n_, k_]:= LCM@@Range[2*n+2]/(LCM@@Range[2*k+2]);
A120107[n_]:= Sum[A120105[n-k, k], {k, 0, Floor[n/2]}];
Table[A120107[n], {n,0,50}] (* G. C. Greubel, May 04 2023 *)

PARI

a(n) = sum(k=0, n\2, lcm([1..2*(n-k)+2])/lcm([1..2*k+2])); \\ Michel Marcus, Mar 04 2019

SageMath

def f(n): return lcm(range(1,2*n+3))
def A120107(n):
    return sum(f(n-k)/f(k) for k in range(1+(n//2)))
[A120107(n) for n in range(51)] # G. C. Greubel, May 04 2023

Formula

a(n) = Sum_{k=0..floor(n/2)} A120105(n-k, k). - G. C. Greubel, May 04 2023