A193789 - OEIS

%I #7 Apr 25 2013 17:23:34

%S 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 729,1,12,60,160,240,192,64,2187,1,14,84,280,560,672,448,128,6561,1,

%U 16,112,448,1120,1792,1792,1024,256,19683,1,18,144,672,2016,4032

%N Mirror of the triangle A193788.

%C A193789 is obtained by reversing the rows of the triangle A193788.

%F Write w(n,k) for the triangle at A193788.  The triangle at A193789 is then given by w(n,n-k).

%e First six rows:

%e 1

%e 1....1

%e 3....1....2

%e 9....1....4....4

%e 27...1....6....12...8

%e 81...1....8....24...32...16

%t z = 10; a = 1; 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}]]  (* A193788 *)

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

%t Flatten[Table[g[n], {n, -1, z}]]  (* A193789 *)

%Y Cf. A193788, A038207.

%K nonn,tabl

%O 0,4

%A _Clark Kimberling_, Aug 05 2011