A167583 A triangle related to the GF(z) formulas of the rows of the ED3 array A167572.

1, 1, 5, 3, 14, 23, 15, 81, 73, 167, 105, 660, 414, 804, 1473, 945, 6825, 2850, 7578, 7629, 16413, 10395, 85050, 19425, 99420, 61389, 111882, 211479, 135135, 1237005, 59535, 1642725, 429525, 1461375, 1518525, 3192975, 2027025, 20540520, -2619540

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 ED3 array A167572. The polynomials in their numerators lead to the triangle given above.

Examples

			Row 1: GF(z) = 1/(1-z).
Row 2: GF(z) = (z + 5)/(1-z)^2.
Row 3: GF(z) = (3*z^2 + 14*z + 23)/(1-z)^3.
Row 4: GF(z) = (15*z^3 + 81*z^2 + 73*z + 167)/(1-z)^4.
Row 5: GF(z) = (105*z^4 + 660*z^3 + 414*z^2 + 804*z + 1473)/(1-z)^5.
Row 6: GF(z) = (945*z^5 + 6825*z^4 + 2850*z^3 + 7578*z^2 + 7629*z + 16413)/(1-z)^6.
Row 7: GF(z) = (10395*z^6 + 85050*z^5 + 19425*z^4 + 99420*z^3 + 61389*z^2 + 111882*z + 211479)/(1-z)^7.
Row 8: GF(z) = (135135*z^7 + 1237005*z^6 + 59535*z^5 + 1642725*z^4 + 429525*z^3 + 1461375*z^2 + 1518525*z + 3192975)/(1-z)^8.
Row 9: GF(z) = (2027025*z^8 + 20540520*z^7 - 2619540*z^6 + 32228280*z^5 - 2479050*z^4 + 27797400*z^3 + 15813900*z^2 + 28153800*z + 54010305)/(1-z)^9.
Row 10: GF(z) = (34459425*z^9 + 383107725*z^8 - 115135020*z^7 + 722119860*z^6 - 283607730*z^5 + 703347750*z^4 + 89576100*z^3 + 470110500*z^2 + 495868185*z + 1030249845)/(1-z)^10.
		

Crossrefs

A167572 is the ED3 array.

A001147 equals the first left hand column.

A167576 equals the first right hand column.

A014481 equals the row sums.