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

1,2

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.

Links

Table of n, a(n) for n=1..36.

Example

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.

Sequence in context: A037290 A155936 A377296 * A108462 A327859 A343824

Adjacent sequences: A167591 A167592 A167593 * A167595 A167596 A167597

Keyword

sign,tabl

Author

Johannes W. Meijer, Nov 10 2009

Status

approved