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%I #6 Jun 16 2016 23:27:41
%S 1,0,2,2,-2,6,0,16,-16,24,24,-48,144,-120,120,0,432,-864,1392,-960,
%T 720,720,-2160,8208,-12816,14448,-8400,5040,0,23040,-69120,149760,
%U -184320,161280,-80640,40320,40320,-161280,760320,-1716480,2684160,-2695680
%N A triangle related to the GF(z) formulas of the rows of the ED2 array A167560.
%C The GF(z) formulas given below correspond to the first ten rows of the ED2 array A167560. The polynomials in their numerators lead to the triangle given above.
%e Row 1: GF(z) = 1/(1-z).
%e Row 2: GF(z) = 2/(1-z)^2.
%e Row 3: GF(z) = (2*z^2 - 2*z + 6)/(1-z)^3.
%e Row 4: GF(z) = (0*z^3 + 16*z^2 - 16*z + 24)/(1-z)^4.
%e Row 5: GF(z) = (24*z^4 - 48*z^3 + 144*z^2 - 120*z + 120)/(1-z)^5.
%e Row 6: GF(z) = (432*z^4 - 864*z^3 + 1392*z^2 - 960*z + 720)/(1-z)^6.
%e Row 7: GF(z) = (720*z^6 - 2160*z^5 + 8208*z^4 - 12816*z^3 + 14448*z^2 - 8400*z + 5040)/(1-z)^7.
%e Row 8: GF(z) = (0*z^7 + 23040*z^6 - 69120*z^5 + 149760*z^4 - 184320*z^3 + 161280*z^2 - 80640*z + 40320)/(1-z)^8.
%e Row 9: GF(z) = (40320*z^8 - 161280*z^7 + 760320*z^6 - 1716480*z^5 + 2684160*z^4 - 2695680*z^3 + 1935360*z^2 - 846720*z + 362880)/(1-z)^9.
%e Row 10: GF(z) = (0*z^9 + 2016000*z^8 - 8064000*z^7 + 22464000*z^6 - 39168000*z^5 + 48360960*z^4 - 40849920*z^3 + 24917760*z^2 - 9676800*z + 3628800)/(1-z)^10.
%Y A167560 is the ED2 array.
%Y A005359 equals the first left hand column.
%Y A000142(n=>1) and 2*A005990 equal the first two right hand columns.
%Y A000142(n=>1) equals the row sums.
%K sign,tabl
%O 1,3
%A _Johannes W. Meijer_, Nov 10 2009
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