OFFSET
0,6
FORMULA
The partial Bell polynomials Y_{2*n, k}(Z) applied to the list Z of the aerated swinging factorials (A056040).
EXAMPLE
Triangle starts:
[0] 1;
[1] 0, 1;
[2] 0, 1, 3;
[3] 0, 2, 15, 15;
[4] 0, 6, 91, 210, 105;
[5] 0, 6, 690, 2835, 3150, 945;
[6] 0, 30, 5214, 42405, 79695, 51975, 10395;
[7] 0, 20, 44772, 666666, 2057055, 2207205, 945945, 135135;
MATHEMATICA
Swing[n_] := n! / Floor[n/2]!^2;
Z[n_] := Flatten[Table[{0, Swing[j]}, {j, 0, n}]];
T[n_, k_] := BellY[2 n, k, Z[n - k]];
Table[T[n, k], {n, 0, 8}, {k, 0, n}] // Flatten
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Mar 13 2022
STATUS
approved