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
Links
- Muniru A Asiru, Table of n, a(n) for n = 0..1000
Programs
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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
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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
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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 *)
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PARI
a(n) = sum(k=0, n\2, lcm([1..2*(n-k)+2])/lcm([1..2*k+2])); \\ Michel Marcus, Mar 04 2019
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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
Comments