A106342 Matrix inverse of A008278, which is the reflected triangle of the Stirling numbers of 2nd kind.

1, -1, 1, 2, -3, 1, -9, 15, -7, 1, 94, -160, 80, -15, 1, -2220, 3790, -1915, 375, -31, 1, 114456, -195461, 98875, -19460, 1652, -63, 1, -12542341, 21419587, -10836231, 2133635, -181559, 7035, -127, 1, 2868686486, -4899099640, 2478483560, -488022556, 41534164, -1611120, 29360, -255, 1

Offset: 0

Author

Paul D. Hanna, May 01 2005

Keywords

• sign
• tabl

Examples

			Triangle T begins:
          1;
         -1,        1;
          2,       -3,         1;
         -9,       15,        -7,       1;
         94,     -160,        80,     -15,       1;
      -2220,     3790,     -1915,     375,     -31,    1;
     114456,  -195461,     98875,  -19460,    1652,  -63,    1;
  -12542341, 21419587, -10836231, 2133635, -181559, 7035, -127, 1;
		

Crossrefs

Row sums are A000007.

Column 0 is A106343.

Cf. A008278, A106340.

Programs

PARI

{T(n,k)=(matrix(n+1,n+1,r,c,if(r>=c, sum(m=0,r-c+1,(-1)^(r-c+1-m)*m^r/m!/(r-c+1-m)!)))^-1)[n+1,k+1]}

Formula

T(n, k) = (Stirling2(n, n-k))^[-1], where T^[-1] denotes the matrix inverse of T.