OFFSET
1,5
COMMENTS
Signed version of the transform (with -1, -2, -3, ... in the subdiagonal) gives A094587 having row sums A000522: (1, 2, 5, 16, 65, 236, ...). Unsigned inverse gives signed A094587 (with alternate signs); giving row sums = a signed variation of A094587 as follows: (1, 0, 1, -2, 9, -44, 265, -1854, ...). Binomial transform of the triangle = A093375.
Eigensequence of the triangle = A000085 starting (1, 2, 4, 10, 26, 76, ...). - Gary W. Adamson, Dec 29 2008
FORMULA
Infinite lower triangular matrix with (1,1,1,...) in the main diagonal and (1,2,3,...) in the subdiagonal.
T(n,n)=1, T(n,n-1)=n-1 and T(n,k)=0 for 1<=k<=n, 1<=n. - Hartmut F. W. Hoft, Jun 10 2017
EXAMPLE
First few rows of the triangle are:
1;
1, 1;
0, 2, 1;
0, 0, 3, 1;
0, 0, 0, 4, 1;
0, 0, 0, 0, 5, 1;
0, 0, 0, 0, 0, 6, 1;
0, 0, 0, 0, 0, 0, 7, 1;
...
MATHEMATICA
a128229[n_] := Table[Which[r==q, 1, r-1==q, q, True, 0], {r, 1, n}, {q, 1, r}]
Flatten[a128229[13]] (* data *)
TableForm[a128229[8]] (* triangle *)
(* Hartmut F. W. Hoft, Jun 10 2017 *)
PROG
(Python)
def T(n, k): return 1 if n==k else n - 1 if k==n - 1 else 0
for n in range(1, 11): print([T(n, k) for k in range(1, n + 1)]) # Indranil Ghosh, Jun 10 2017
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Feb 19 2007
STATUS
approved