A167583 - OEIS

%I #6 Jun 17 2016 00:09:43

%S 1,1,5,3,14,23,15,81,73,167,105,660,414,804,1473,945,6825,2850,7578,

%T 7629,16413,10395,85050,19425,99420,61389,111882,211479,135135,

%U 1237005,59535,1642725,429525,1461375,1518525,3192975,2027025,20540520,-2619540

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

%C 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.

%e Row 1: GF(z) = 1/(1-z).

%e Row 2: GF(z) = (z + 5)/(1-z)^2.

%e Row 3: GF(z) = (3*z^2 + 14*z + 23)/(1-z)^3.

%e Row 4: GF(z) = (15*z^3 + 81*z^2 + 73*z + 167)/(1-z)^4.

%e Row 5: GF(z) = (105*z^4 + 660*z^3 + 414*z^2 + 804*z + 1473)/(1-z)^5.

%e Row 6: GF(z) = (945*z^5 + 6825*z^4 + 2850*z^3 + 7578*z^2 + 7629*z + 16413)/(1-z)^6.

%e 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.

%e 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.

%e 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.

%e 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.

%Y A167572 is the ED3 array.

%Y A001147 equals the first left hand column.

%Y A167576 equals the first right hand column.

%Y A014481 equals the row sums.

%K sign,tabl

%O 1,3

%A _Johannes W. Meijer_, Nov 10 2009