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
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;
Programs
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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.