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%I #3 Mar 30 2012 18:36:46
%S 1,-1,1,2,-3,1,-9,15,-7,1,94,-160,80,-15,1,-2220,3790,-1915,375,-31,1,
%T 114456,-195461,98875,-19460,1652,-63,1,-12542341,21419587,-10836231,
%U 2133635,-181559,7035,-127,1,2868686486,-4899099640,2478483560,-488022556,41534164,-1611120,29360,-255,1
%N Matrix inverse of A008278, which is a triangle of Stirling numbers of 2nd kind.
%C Column 0 is A106343. Row sums are zero after the initial row.
%e Triangle T begins:
%e 1;
%e -1,1;
%e 2,-3,1;
%e -9,15,-7,1;
%e 94,-160,80,-15,1;
%e -2220,3790,-1915,375,-31,1;
%e 114456,-195461,98875,-19460,1652,-63,1;
%e -12542341,21419587,-10836231,2133635,-181559,7035,-127,1; ...
%e Matrix inverse is A008278 and begins:
%e 1;
%e 1,1;
%e 1,3,1;
%e 1,6,7,1;
%e 1,10,25,15,1; ...
%o (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]}
%Y Cf. A008278, A106340, A106343.
%K sign,tabl
%O 0,4
%A _Paul D. Hanna_, May 01 2005
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