OFFSET
0,6
LINKS
FORMULA
T(n,k) = Sum_{t=0..k} C(n,k-t) * Stirling2(n-(k-t),t) * t^(k-t).
E.g.f.: exp(y*exp(x*y)*(exp(x)-1)). - Vladeta Jovovic, Dec 08 2008
EXAMPLE
T(3,2) = 6: {1,2}{3}, {1,3}{2}, {2,3}{1}, {1,2}<-3, {1,3}<-2, {2,3}<-1.
Triangle begins:
1;
0, 1;
0, 1, 3;
0, 1, 6, 10;
0, 1, 11, 36, 41;
0, 1, 20, 105, 230, 196;
0, 1, 37, 285, 955, 1560, 1057;
0, 1, 70, 756, 3535, 8680, 11277, 6322;
...
MAPLE
T:= (n, k)-> add(binomial(n, k-t)*Stirling2(n-(k-t), t)*t^(k-t), t=0..k):
seq(seq(T(n, k), k=0..n), n=0..11);
MATHEMATICA
T[n_, k_] := Sum[Binomial[n, k-t]*StirlingS2[n - (k-t), t]*t^(k-t), {t, 0, k}]; T[0, 0] = 1; T[_, 0] = 0;
Table[T[n, k], {n, 0, 11}, {k, 0, n}] // Flatten (* Jean-François Alcover, May 31 2016, translated from Maple *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Aug 12 2008
STATUS
approved