A167568 A triangle related to the GF(z) formulas of the rows of the ED2 array A167560.

1, 0, 2, 2, -2, 6, 0, 16, -16, 24, 24, -48, 144, -120, 120, 0, 432, -864, 1392, -960, 720, 720, -2160, 8208, -12816, 14448, -8400, 5040, 0, 23040, -69120, 149760, -184320, 161280, -80640, 40320, 40320, -161280, 760320, -1716480, 2684160, -2695680

Offset: 1

Author

Johannes W. Meijer, Nov 10 2009

Keywords

• sign
• tabl

Comments

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.

Examples

			Row 1: GF(z) = 1/(1-z).
Row 2: GF(z) = 2/(1-z)^2.
Row 3: GF(z) = (2*z^2 - 2*z + 6)/(1-z)^3.
Row 4: GF(z) = (0*z^3 + 16*z^2 - 16*z + 24)/(1-z)^4.
Row 5: GF(z) = (24*z^4 - 48*z^3 + 144*z^2 - 120*z + 120)/(1-z)^5.
Row 6: GF(z) = (432*z^4 - 864*z^3 + 1392*z^2 - 960*z + 720)/(1-z)^6.
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.
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.
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.
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.
		

Crossrefs

A167560 is the ED2 array.

A005359 equals the first left hand column.

A000142(n=>1) and 2*A005990 equal the first two right hand columns.

A000142(n=>1) equals the row sums.