%I #20 May 05 2023 01:43:48
%S 1,6,31,425,1331,14084,182533,390855,6192220,117429752,136000866,
%T 2700408581,13835919839,42477252404,1171690228133,72397239805085,
%U 84274330442804,86644937313210,2686078920033439,3119346038772923
%N a(n) = Sum_{k=0..floor(n/2)} lcm(1,...,2*(n-k)+2)/lcm(1,...,2*k+2).
%C Diagonal sums of number triangle A120101.
%H Muniru A Asiru, <a href="/A120107/b120107.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = Sum_{k=0..floor(n/2)} A120105(n-k, k). - _G. C. Greubel_, May 04 2023
%t A120105[n_, k_]:= LCM@@Range[2*n+2]/(LCM@@Range[2*k+2]);
%t A120107[n_]:= Sum[A120105[n-k, k], {k, 0, Floor[n/2]}];
%t Table[A120107[n], {n,0,50}] (* _G. C. Greubel_, May 04 2023 *)
%o (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
%o (PARI) a(n) = sum(k=0, n\2, lcm([1..2*(n-k)+2])/lcm([1..2*k+2])); \\ _Michel Marcus_, Mar 04 2019
%o (Magma)
%o A120105:= func< n,k | Lcm([1..2*n+2])/Lcm([1..2*k+2]) >;
%o [(&+[A120105(n-k,k): k in [0..Floor(n/2)]]): n in [0..50]]; // _G. C. Greubel_, May 04 2023
%o (SageMath)
%o def f(n): return lcm(range(1,2*n+3))
%o def A120107(n):
%o return sum(f(n-k)/f(k) for k in range(1+(n//2)))
%o [A120107(n) for n in range(51)] # _G. C. Greubel_, May 04 2023
%Y Cf. A120101, A120105, A120106.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Jun 09 2006