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%I #5 Mar 30 2012 18:57:38
%S 1,1,1,5,3,2,25,9,12,4,125,27,54,36,8,625,81,216,216,96,16,3125,243,
%T 810,1080,720,240,32,15625,729,2916,4860,4320,2160,576,64,78125,2187,
%U 10206,20412,22680,15120,6048,1344,128,390625,6561,34992,81648,108864
%N Mirror of the triangle A193798.
%C A193799 is obtained by reversing the rows of the triangle A193798.
%F Write w(n,k) for the triangle at A193798. The triangle at A193799 is then given by w(n,n-k).
%e First six rows:
%e 1
%e 1.....1
%e 5.....3....2
%e 25....9....12....4
%e 125...27...54....36...8
%e 625...81...216...216..96..16
%t z = 8; a = 3; b = 2;
%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}]] (* A193798 *)
%t TableForm[Table[g[n], {n, -1, z}]]
%t Flatten[Table[g[n], {n, -1, z}]] (* A193799 *)
%Y Cf. A193798.
%K nonn,tabl
%O 0,4
%A _Clark Kimberling_, Aug 05 2011
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