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%I #5 Mar 30 2012 18:57:39
%S 1,1,2,3,6,4,7,14,12,8,15,30,28,24,16,31,62,60,56,48,32,63,126,124,
%T 120,112,96,64,127,254,252,248,240,224,192,128,255,510,508,504,496,
%U 480,448,384,256,511,1022,1020,1016,1008,992,960,896,768,512,1023,2046
%N Mirror of the triangle A193902.
%C A193903 is obtained by reversing the rows of the triangle A193902.
%F Write w(n,k) for the triangle at A193902. The triangle at A193903 is then given by w(n,n-k).
%e First six rows:
%e 1
%e 1....2
%e 3....6....4
%e 7....14...12...8
%e 15...30...28...24...16
%e 31...62...60...56...48...32
%t z = 12;
%t p[n_, x_] := x*p[n - 1, x] + 2^n; p[0, x_] := 1;
%t q[n_, x_] := 2 x*q[n - 1, x] + 1; q[0, x_] := 1;
%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}]] (* A193902 *)
%t TableForm[Table[g[n], {n, -1, z}]]
%t Flatten[Table[g[n], {n, -1, z}]] (* A193903 *)
%Y Cf. A193902.
%K nonn,tabl
%O 0,3
%A _Clark Kimberling_, Aug 08 2011
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