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A120107
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a(n) = Sum_{k=0..floor(n/2)} lcm(1,...,2*(n-k)+2)/lcm(1,...,2*k+2).
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3
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1, 6, 31, 425, 1331, 14084, 182533, 390855, 6192220, 117429752, 136000866, 2700408581, 13835919839, 42477252404, 1171690228133, 72397239805085, 84274330442804, 86644937313210, 2686078920033439, 3119346038772923
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OFFSET
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0,2
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COMMENTS
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Diagonal sums of number triangle A120101.
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LINKS
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FORMULA
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MATHEMATICA
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A120105[n_, k_]:= LCM@@Range[2*n+2]/(LCM@@Range[2*k+2]);
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PROG
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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
(PARI) a(n) = sum(k=0, n\2, lcm([1..2*(n-k)+2])/lcm([1..2*k+2])); \\ Michel Marcus, Mar 04 2019
(Magma)
A120105:= func< n, k | Lcm([1..2*n+2])/Lcm([1..2*k+2]) >;
(SageMath)
def f(n): return lcm(range(1, 2*n+3))
return sum(f(n-k)/f(k) for k in range(1+(n//2)))
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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