A078921 Signed variant of A077012.

1, -1, 2, 2, -3, 6, -6, 8, -12, 24, 24, -30, 40, -60, 120, -120, 144, -180, 240, -360, 720, 720, -840, 1008, -1260, 1680, -2520, 5040, -5040, 5760, -6720, 8064, -10080, 13440, -20160, 40320, 40320, -45360, 51840, -60480, 72576, -90720, 120960, -181440, 362880, -362880, 403200, -453600, 518400, -604800, 725760, -907200, 1209600, -1814400, 3628800

Offset: 1

Author

Wouter Meeussen, Dec 14 2002

Keywords

• easy
• sign
• tabl

Comments

Row sums give A024167.

Examples

			Triangle starts:
     1
    -1,    2
     2,   -3,    6
    -6,    8,  -12,    24
    24,  -30,   40,   -60,  120
  -120,  144, -180,   240, -360,   720
   720, -840, 1008, -1260, 1680, -2520, 5040
  ...
		

Crossrefs

Cf. A000254, A024167, A077012, A078922.

Programs

Mathematica

Table[Table[ -(-1)^(n-k+1) n/(n-k+1), {k, 1, n}] (n-1)!, {n, 1, 12}]

Formula

T(n, k) = -(-1)^(n-k+1)*(n/(n-k+1))*(n-1)!.

E.g.f.: log(1+x)/(1-y*x). - Vladeta Jovovic, Feb 07 2003

Sum_{n>=1} Sum_{k=1..n} 1/T(n, k) = (e^2+1)/(4*e). - Amiram Eldar, Jun 29 2025