OFFSET
0,5
LINKS
Alois P. Heinz, Rows n = 0..140, flattened
FORMULA
E.g.f. of column k: x^k * Product_{i=1..k} (i-1)!/(i!-x^i).
EXAMPLE
T(3,1) = 6: 1|2|3, 1|3|2, 2|1|3, 2|3|1, 3|1|2, 3|2|1.
T(3,2) = 3: 1|23, 2|13, 3|12.
T(3,3) = 1: 123.
Triangle T(n,k) begins:
1;
0, 1;
0, 2, 1;
0, 6, 3, 1;
0, 24, 18, 4, 1;
0, 120, 90, 30, 5, 1;
0, 720, 630, 200, 45, 6, 1;
0, 5040, 4410, 1610, 350, 63, 7, 1;
0, 40320, 37800, 13440, 3290, 560, 84, 8, 1;
MAPLE
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
b(n, i-1)+`if`(i>n, 0, binomial(n, i)*b(n-i, i))))
end:
T:= (n, k)-> b(n, k) -`if`(k=0, 0, b(n, k-1)):
seq(seq(T(n, k), k=0..n), n=0..12);
MATHEMATICA
b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, b[n, i - 1] + If[i > n, 0, Binomial[n, i]*b[n - i, i]]]]; T[n_, k_] := b[n, k] - If[k == 0, 0, b[n, k - 1]]; Table[T[n, k], {n, 0, 12}, {k, 0, n}] // Flatten (* Jean-François Alcover, Dec 12 2016, Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Sep 10 2015
STATUS
approved