OFFSET
1,11
COMMENTS
Every row sums to 1.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..1275 (first 50 rows)
FORMULA
T(n,k) = Sum_{i=k..n} A054525(i,k).
A002088(n) = Sum_{k=1..n} k*T(n,k).
Recurrence: T(n, k) = If n >= k then If k = 1 then 1 - Sum_{i=1..n-1} T(n, k + i)/(i + 1)^(s - 1) else T(floor(n/k) else 1)) else 0). - Mats Granvik, Apr 17 2016
EXAMPLE
First few rows of the triangle:
1;
0, 1;
-1, 1, 1;
-1, 0, 1, 1;
-2, 0, 1, 1, 1;
-1, -1, 0, 1, 1, 1;
-2, -1, 0, 1, 1, 1, 1;
-2, -1, 0, 0, 1, 1, 1, 1;
-2, -1, -1, 0, 1, 1, 1, 1, 1;
-1, -2, -1, 0, 0, 1, 1, 1, 1, 1;
...
MATHEMATICA
Clear[t, s, n, k, z, x]; z = 1; nn = 10; t[n_, k_] := t[n, k] = If[n >= k, If[k == 1, 1 - Sum[t[n, k + i]/(i + 1)^(s - 1), {i, 1, n - 1}], t[Floor[n/k], 1]], 0]; Flatten[Table[Table[Limit[t[n, k], s -> z], {k, 1, n}], {n, 1, nn}]] (* Mats Granvik, Jul 22 2012 *) (* updated Mats Granvik, Apr 10 2016 *)
PROG
(PARI) T(n, k) = sum(i=1, n\k, moebius(i)) \\ Andrew Howroyd, Sep 20 2025
CROSSREFS
KEYWORD
tabl,sign
AUTHOR
Gary W. Adamson, Oct 31 2007
EXTENSIONS
More terms from Amiram Eldar, Jun 09 2024
New name from Andrew Howroyd, Sep 20 2025
STATUS
approved
