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A193789 Mirror of the triangle A193788.

%I A193789 #7 Apr 25 2013 17:23:34
%S A193789 1,1,1,3,1,2,9,1,4,4,27,1,6,12,8,81,1,8,24,32,16,243,1,10,40,80,80,32,
%T A193789 729,1,12,60,160,240,192,64,2187,1,14,84,280,560,672,448,128,6561,1,
%U A193789 16,112,448,1120,1792,1792,1024,256,19683,1,18,144,672,2016,4032
%N A193789 Mirror of the triangle A193788.
%C A193789 A193789 is obtained by reversing the rows of the triangle A193788.
%F A193789 Write w(n,k) for the triangle at A193788.  The triangle at A193789 is then given by w(n,n-k).
%e A193789 First six rows:
%e A193789 1
%e A193789 1....1
%e A193789 3....1....2
%e A193789 9....1....4....4
%e A193789 27...1....6....12...8
%e A193789 81...1....8....24...32...16
%t A193789 z = 10; a = 1; b = 2;
%t A193789 p[n_, x_] := (a*x + b)^n
%t A193789 q[n_, x_] := 1 + x^n ; q[n_, 0] := q[n, x] /. x -> 0;
%t A193789 t[n_, k_] := Coefficient[p[n, x], x^k]; t[n_, 0] := p[n, x] /. x -> 0;
%t A193789 w[n_, x_] := Sum[t[n, k]*q[n + 1 - k, x], {k, 0, n}]; w[-1, x_] := 1
%t A193789 g[n_] := CoefficientList[w[n, x], {x}]
%t A193789 TableForm[Table[Reverse[g[n]], {n, -1, z}]]
%t A193789 Flatten[Table[Reverse[g[n]], {n, -1, z}]]  (* A193788 *)
%t A193789 TableForm[Table[g[n], {n, -1, z}]]
%t A193789 Flatten[Table[g[n], {n, -1, z}]]  (* A193789 *)
%Y A193789 Cf. A193788, A038207.
%K A193789 nonn,tabl
%O A193789 0,4
%A A193789 _Clark Kimberling_, Aug 05 2011