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A373167
Triangle read by rows: the exponential almost-Riordan array ( 1/(1-x) | exp(x^2), 2*x ).
0
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, 40320, 0, 1680, 0, 3360, 0, 1344, 0, 128, 362880, 1680, 0, 13440, 0, 13440, 0, 3584, 0, 256, 3628800, 0, 30240, 0, 80640, 0, 48384, 0, 9216, 0, 512
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
Cf. A011782 (right diagonal), A000142 (k=0), A001813.
Sequence in context: A139213 A344873 A306079 * A242860 A320239 A033727
KEYWORD
nonn,tabl
AUTHOR
Stefano Spezia, May 26 2024
STATUS
approved