A167594 A triangle related to the GF(z) formulas of the rows of the ED4 array A167584.

1, 2, 2, 9, 2, 13, 60, -12, 68, 76, 525, -300, 774, 132, 789, 5670, -5250, 11820, -3636, 6702, 7734, 72765, -92610, 212415, -143340, 143307, 19086, 110937, 1081080, -1746360, 4286520, -4246200, 4156200, -1204200, 1305000, 1528920

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 ED4 array A167584. The polynomials in their numerators lead to the triangle given above.

Examples

			Row 1: GF(z) = 1/(1-z).
Row 2: GF(z) = (2*z + 2)/(1-z)^2.
Row 3: GF(z) = (9*z^2 + 2*z + 13)/(1-z)^3.
Row 4: GF(z) = (60*z^3 - 12*z^2 + 68*z + 76)/(1-z)^4.
Row 5: GF(z) = (525*z^4 - 300*z^3 + 774*z^2 + 132*z + 789)/(1-z)^5.
Row 6: GF(z) = (5670*z^5 - 5250*z^4 + 11820*z^3 - 3636*z^2 + 6702*z + 7734)/(1-z)^6.
Row 7: GF(z) = (72765*z^6 - 92610*z^5 + 212415*z^4 - 143340*z^3 + 143307*z^2 + 19086*z + 110937)/ (1-z)^7.
Row 8: GF(z) = (1081080*z^7 - 1746360*z^6 + 4286520*z^5 - 4246200*z^4 + 4156200*z^3 - 1204200*z^2 + 1305000*z + 1528920)/(1-z)^8.
Row 9: GF(z) = (18243225*z^8 - 35675640*z^7 + 95176620*z^6 -121723560*z^5 + 132769350*z^4 - 73816200*z^3 + 45017100*z^2 + 4887720*z + 28018665) / (1-z)^9.
Row 10: GF(z) = (344594250*z^9 - 790539750*z^8 + 2299457160*z^7 - 3567314520*z^6 + 4441299660*z^5 - 3398138100*z^4 + 2160066600*z^3 - 550619640*z^2 + 421244730*z + 497895210)/(1-z)^10.
		

Crossrefs

A167584 is the ED4 array.

A001193 equals the first left hand column.

A024199 equals the first right hand column.

A002866 equals the row sums.