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

0,2

Links

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

Formula

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

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 *)

Prog

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

Crossrefs

Cf. A120108, A120109.

Sequence in context: A279286 A282197 A050612 * A047694 A338399 A262016

Adjacent sequences: A120107 A120108 A120109 * A120111 A120112 A120113

Keyword

easy,nonn

Author

Paul Barry, Jun 09 2006

Status

approved