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%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
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