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Mirror of the triangle A193794.
2

%I #5 Mar 30 2012 18:57:38

%S 1,1,1,4,3,1,16,9,6,1,64,27,27,9,1,256,81,108,54,12,1,1024,243,405,

%T 270,90,15,1,4096,729,1458,1215,540,135,18,1,16384,2187,5103,5103,

%U 2835,945,189,21,1,65536,6561,17496,20412,13608,5670,1512,252,24,1,262144

%N Mirror of the triangle A193794.

%C A193795 is obtained by reversing the rows of the triangle A193794.

%F Write w(n,k) for the triangle at A193794. The triangle at A193795 is then given by w(n,n-k).

%e First six rows:

%e 1

%e 1.....1

%e 4.....3....1

%e 16....9....6....1

%e 64....27...27...9...1

%e 256...81...108..54..12...1

%t z = 9; a = 3; b = 1;

%t p[n_, x_] := (a*x + b)^n

%t q[n_, x_] := 1 + x^n ; q[n_, 0] := q[n, x] /. x -> 0;

%t t[n_, k_] := Coefficient[p[n, x], x^k]; t[n_, 0] := p[n, x] /. x -> 0;

%t w[n_, x_] := Sum[t[n, k]*q[n + 1 - k, x], {k, 0, n}]; w[-1, x_] := 1

%t g[n_] := CoefficientList[w[n, x], {x}]

%t TableForm[Table[Reverse[g[n]], {n, -1, z}]]

%t Flatten[Table[Reverse[g[n]], {n, -1, z}]] (* A193794 *)

%t TableForm[Table[g[n], {n, -1, z}]]

%t Flatten[Table[g[n], {n, -1, z}]] (* A193795 *)

%Y Cf. A193794.

%K nonn,tabl

%O 0,4

%A _Clark Kimberling_, Aug 05 2011