OFFSET
0,4
COMMENTS
Row sums = n^n, all functions f:{1,2,...,n}->{1,2,...,n}.
T(n,n)= n!, bijections on {1,2,...,n}.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..140, flattened
FORMULA
E.g.f.: Sum_{k=0..n} T(n,k) * y^k * x^n / n! = (exp(x) - x + y*x)^n.
EXAMPLE
Triangle T(n,k) begins:
1;
0 1;
2 0 2;
3 18 0 6;
40 48 144 0 24;
205 1000 600 1200 0 120;
...
MAPLE
with(combinat): C:= binomial:
b:= proc(t, i, u) option remember; `if`(t=0, 1,
`if`(i<2, 0, b(t, i-1, u) +add(multinomial(t, t-i*j, i$j)
*b(t-i*j, i-1, u-j)*u!/(u-j)!/j!, j=1..t/i)))
end:
T:= (n, k)-> C(n, k)*C(n, k)*k! *b(n-k$2, n-k):
seq(seq(T(n, k), k=0..n), n=0..10); # Alois P. Heinz, Nov 13 2013
MATHEMATICA
nn = 8; Prepend[CoefficientList[Table[n! Coefficient[Series[(Exp[x] - x + y x)^n, {x, 0, nn}], x^n], {n, 1, nn}], y], {1}] // Flatten
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Geoffrey Critzer, Feb 12 2012
STATUS
approved