A106342 Matrix inverse of A008278, which is a triangle of 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

Comments

Column 0 is A106343. Row sums are zero after the initial row.

Links

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

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; ...
Matrix inverse is A008278 and begins:
1;
1,1;
1,3,1;
1,6,7,1;
1,10,25,15,1; ...

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

Cf. A008278, A106340, A106343.

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