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

0,4

Links

Table of n, a(n) for n=0..44.

Formula

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

Example

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;

Prog

(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]}

Crossrefs

Row sums are A000007.

Column 0 is A106343.

Cf. A008278, A106340.

Sequence in context: A117025 A078021 A300838 * A247563 A322702 A107855

Adjacent sequences: A106339 A106340 A106341 * A106343 A106344 A106345

Keyword

sign,tabl

Author

Paul D. Hanna, May 01 2005

Status

approved