OFFSET
0,4
LINKS
Y. Alp and E. G. Kocer, Exponential Almost-Riordan Arrays, Results Math 79, 173 (2024). See page 10.
FORMULA
T(n,0) = n!; T(n,k) = (n-1)!/(k-1)! * [x^(n-1)] exp(x^2)*(2*x)^(k-1).
EXAMPLE
The triangle begins:
1;
1, 1;
2, 0, 2;
6, 2, 0, 4;
24, 0, 12, 0, 8;
120, 12, 0, 48, 0, 16;
720, 0, 120, 0, 160, 0, 32;
5040, 120, 0, 720, 0, 480, 0, 64;
...
MATHEMATICA
T[n_, 0]:=n!; T[n_, k_]:=(n-1)!/(k-1)!SeriesCoefficient[Exp[x^2](2x)^(k-1), {x, 0, n-1}]; Table[T[n, k], {n, 0, 10}, {k, 0, n}]//Flatten
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Stefano Spezia, May 26 2024
STATUS
approved