A120110 Diagonal sums of number triangle A120108.

1, 2, 7, 15, 67, 92, 461, 1065, 3016, 3956, 29478, 42231, 379107, 547556, 603421, 991923, 12709228, 18540622, 241033695, 352271227, 389226278, 407797820, 5532937710, 8097345425, 30368363481, 41503874738, 98701094676, 127342427241

Offset: 0

Author

Paul Barry, Jun 09 2006

Keywords

• easy
• nonn

Links

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

Crossrefs

Cf. A120108, A120109.

Programs

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

Magma

A120108:= func< n,k | Lcm([1..n+1])/Lcm([1..k+1]) >;
[(&+[A120108(n-k,k): k in [0..Floor(n/2)]]): n in [0..50]]; // G. C. Greubel, May 04 2023

Mathematica

A120108[n_, k_]:= LCM@@Range[n+1]/(LCM@@Range[k+1]);
A120110[n_]:= Sum[A120108[n-k,k], {k,0,n/2}];
Table[A120110[n], {n,0,50}] (* G. C. Greubel, May 04 2023 *)

PARI

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

SageMath

def f(n): return lcm(range(1,n+2))
def A120110(n):
    return sum(f(n-k)//f(k) for k in range((n//2)+1))
[A120110(n) for n in range(51)] # G. C. Greubel, May 04 2023

Formula

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