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URL: https://oeis.org/A142156

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A142156
Triangle T(n,k)= n! if k=0, T(n,k) = -(n-k)!*A003319(k) if k > 0.
0
1, 1, -1, 2, -1, -1, 6, -2, -1, -3, 24, -6, -2, -3, -13, 120, -24, -6, -6, -13, -71, 720, -120, -24, -18, -26, -71, -461, 5040, -720, -120, -72, -78, -142, -461, -3447, 40320, -5040, -720, -360, -312, -426, -922, -3447, -29093, 362880, -40320, -5040, -2160, -1560
OFFSET
0,4
FORMULA
T(n,0) = A000142(n).
T(n,k) = -A141476(n-1,k-1), k > 0.
Sum_{k=0..n} |T(n,k)| = 2*n! = A098558(n).
EXAMPLE
Triangle begins
1;
1, -1;
2, -1, -1;
6, -2, -1, -3;
24, -6, -2, -3, -13;
120, -24, -6, -6, -13, -71;
720, -120, -24, -18, -26, -71, -461;
MATHEMATICA
(* b = A003319 *) b[0]=0; b[n_] := b[n] = n! - Sum[k! b[n-k], {k, 1, n-1}]; T[n_, 0] := n!; T[n_, k_] := -(n - k)! b[k]; Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* Jean-François Alcover, Feb 18 2018 *)
CROSSREFS
Sequence in context: A178249 A114423 A119502 * A136707 A179972 A085826
KEYWORD
sign,tabl
AUTHOR
Paul Curtz, Sep 16 2008
STATUS
approved