OFFSET
0,5
LINKS
Alois P. Heinz, Rows n = 0..140, flattened
FORMULA
EXAMPLE
Triangle T(n,k) begins:
1;
0, 1;
0, 2, 1;
0, 6, 6, 1;
0, 24, 42, 8, 1;
0, 120, 330, 80, 10, 1;
0, 720, 2970, 860, 120, 12, 1;
0, 5040, 30240, 10290, 1540, 168, 14, 1;
0, 40320, 345240, 136080, 21490, 2464, 224, 16, 1;
...
MAPLE
A:= proc(n, k) option remember; `if`(n=0, 1, add(
A(n-i, k)*binomial(n, i), i=1..min(n, k)))
end:
T:= (n, k)-> A(n, k) -`if`(k=0, 0, A(n, k-1)):
seq(seq(T(n, k), k=0..n), n=0..10);
MATHEMATICA
A[n_, k_] := A[n, k] = If[n == 0, 1, Sum[A[n - i, k]*Binomial[n, i], {i, 1, Min[n, k]}]]; T[n_, k_] := A[n, k] - If[k == 0, 0, A[n, k - 1]]; Table[T[n, k], {n, 0, 10}, { k, 0, n}] // Flatten (* Jean-François Alcover, Feb 11 2017, translated from Maple *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Sep 22 2016
STATUS
approved