A193797 - OEIS

%I #6 Mar 30 2012 18:57:38

%S 1,1,1,5,2,3,25,4,12,9,125,8,36,54,27,625,16,96,216,216,81,3125,32,

%T 240,720,1080,810,243,15625,64,576,2160,4320,4860,2916,729,78125,128,

%U 1344,6048,15120,22680,20412,10206,2187,390625,256,3072,16128,48384

%N Mirror of the triangle A193796.

%C A193797 is obtained by reversing the rows of the triangle A193796.

%e Write w(n,k) for the triangle at A193796.  The triangle at A193797 is then given by w(n,n-k).

%e First six rows:

%e 1

%e 1....1

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

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

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

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

%t z = 8; a = 2; 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}]]  (* A193796 *)

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

%t Flatten[Table[g[n], {n, -1, z}]]  (* A193797 *)

%Y Cf. A193796.

%K nonn,tabl

%O 0,4

%A _Clark Kimberling_, Aug 05 2011