OFFSET
1,6
LINKS
Alois P. Heinz, Rows n = 1..142, flattened
Wikipedia, Permutation
FORMULA
EXAMPLE
Triangle T(n,k) begins:
: 1 ;
: 1, 1, 1 ;
: 1, 3, 4, 3, 1 ;
: 1, 5, 13, 15, 13, 5, 1 ;
: 1, 7, 28, 67, 76, 67, 28, 7, 1 ;
: 1, 9, 49, 179, 411, 455, 411, 179, 49, 9, 1 ;
: 1, 11, 76, 375, 1306, 2921, 3186, 2921, 1306, 375, 76, 11, 1 ;
MAPLE
b:= proc(s, d) option remember; (n-> `if`(n=0, add(x^j, j=d),
add(b(s minus {i}, d union {n-i}), i=s)))(nops(s))
end:
T:= n-> (p-> seq(coeff(p, x, i)/abs(i)!, i=1-n..n-1))(b({$1..n}, {})):
seq(T(n), n=1..8);
# second Maple program:
T:= (n, k)-> -add((-1)^j*binomial(n-abs(k), j)*(n-j)!, j=1..n)/abs(k)!:
seq(seq(T(n, k), k=1-n..n-1), n=1..9);
MATHEMATICA
T[n_, k_] := (-1/Abs[k]!) Sum[(-1)^j Binomial[n-Abs[k], j] (n-j)!, {j, 1, n}];
Table[T[n, k], {n, 1, 9}, {k, 1-n, n-1}] // Flatten (* Jean-François Alcover, Feb 15 2021 *)
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Alois P. Heinz, Feb 17 2019
STATUS
approved