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A120110 Diagonal sums of number triangle A120108.

%I A120110 #14 Feb 26 2025 19:22:22
%S A120110 1,2,7,15,67,92,461,1065,3016,3956,29478,42231,379107,547556,603421,
%T A120110 991923,12709228,18540622,241033695,352271227,389226278,407797820,
%U A120110 5532937710,8097345425,30368363481,41503874738,98701094676,127342427241
%N A120110 Diagonal sums of number triangle A120108.
%H A120110 Muniru A Asiru, <a href="/A120110/b120110.txt">Table of n, a(n) for n = 0..1000</a>
%F A120110 a(n) = Sum_{k=0..floor(n/2)} lcm(1,..,n-k+1)/lcm(1,..,k+1).
%t A120110 A120108[n_, k_]:= LCM@@Range[n+1]/(LCM@@Range[k+1]);
%t A120110 A120110[n_]:= Sum[A120108[n-k,k], {k,0,n/2}];
%t A120110 Table[A120110[n], {n,0,50}] (* _G. C. Greubel_, May 04 2023 *)
%o A120110 (GAP) List([0..30],n->Sum([0..Int(n/2)],k->Lcm(List([1..n-k+1],i->i))/Lcm(List([1..k+1],i->i)))); # _Muniru A Asiru_, Mar 04 2019
%o A120110 (PARI) a(n) = sum(k=0, n\2, lcm([1..n-k+1])/lcm([1..k+1])); \\ _Michel Marcus_, Mar 04 2019
%o A120110 (Magma)
%o A120110 A120108:= func< n,k | Lcm([1..n+1])/Lcm([1..k+1]) >;
%o A120110 [(&+[A120108(n-k,k): k in [0..Floor(n/2)]]): n in [0..50]]; // _G. C. Greubel_, May 04 2023
%o A120110 (SageMath)
%o A120110 def f(n): return lcm(range(1,n+2))
%o A120110 def A120110(n):
%o A120110     return sum(f(n-k)//f(k) for k in range((n//2)+1))
%o A120110 [A120110(n) for n in range(51)] # _G. C. Greubel_, May 04 2023
%Y A120110 Cf. A120108, A120109.
%K A120110 easy,nonn
%O A120110 0,2
%A A120110 _Paul Barry_, Jun 09 2006