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

1,3

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.

Links

Table of n, a(n) for n=1..39.

Example

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.

Sequence in context: A367204 A213750 A213774 * A351951 A329029 A248983

Adjacent sequences: A167580 A167581 A167582 * A167584 A167585 A167586

Keyword

sign,tabl

Author

Johannes W. Meijer, Nov 10 2009

Status

approved