A193793 - OEIS

%I #4 Mar 30 2012 18:57:38

%S 1,1,1,4,1,3,16,1,6,9,64,1,9,27,27,256,1,12,54,108,81,1024,1,15,90,

%T 270,405,243,4096,1,18,135,540,1215,1458,729,16384,1,21,189,945,2835,

%U 5103,5103,2187,65536,1,24,252,1512,5670,13608,20412,17496,6561

%N Mirror of the triangle A193792.

%C A193793 is obtained by reversing the rows of the triangle A193792.

%F Write w(n,k) for the triangle at A193792.  The triangle at A193793 is then given by w(n,n-k).

%e First six rows:

%e 1

%e 1....1

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

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

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

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

%t z = 8; a = 1; b = 3;

%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}]]  (* A193792 *)

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

%t Flatten[Table[g[n], {n, -1, z}]]  (* A193793 *)

%Y Cf. A193792.

%K nonn,tabl

%O 0,4

%A _Clark Kimberling_, Aug 05 2011