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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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..49.

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-Fran├žois Alcover, Feb 18 2018 *)

CROSSREFS

Sequence in context: A107106 A178249 A119502 * A136707 A179972 A085826

Adjacent sequences:  A142153 A142154 A142155 * A142157 A142158 A142159

KEYWORD

sign,tabl

AUTHOR

Paul Curtz, Sep 16 2008

STATUS

approved

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Last modified August 20 14:06 EDT 2019. Contains 326152 sequences. (Running on oeis4.)