OFFSET
0,4
LINKS
Y. Alp and E. G. Kocer, Exponential Almost-Riordan Arrays, Results Math 79, 173 (2024). See page 6.
FORMULA
T(n,0) = n!; T(n,k) = (n-1)!/(k-1)! * [x^(n-1)] log(1/(1-x))^(k-1)/(1-x).
T(n,1) = (n-1)! for n > 0.
T(n,2) = A000254(n-1) for n > 1.
EXAMPLE
The triangle begins:
1;
1, 1;
2, 1, 1;
6, 2, 3, 1;
24, 6, 11, 6, 1;
120, 24, 50, 35, 10, 1;
720, 120, 274, 225, 85, 15, 1;
...
MATHEMATICA
T[n_, 0]:=n!; T[n_, k_]:=(n-1)!/(k-1)!SeriesCoefficient[1/(1-x)Log[1/(1-x)]^(k-1), {x, 0, n-1}]; Table[T[n, k], {n, 0, 9}, {k, 0, n}]//Flatten
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Stefano Spezia, May 26 2024
STATUS
approved