A193789 Mirror of the triangle A193788.

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, 729, 1, 12, 60, 160, 240, 192, 64, 2187, 1, 14, 84, 280, 560, 672, 448, 128, 6561, 1, 16, 112, 448, 1120, 1792, 1792, 1024, 256, 19683, 1, 18, 144, 672, 2016, 4032

Offset: 0

Author

Clark Kimberling, Aug 05 2011

Keywords

• nonn
• tabl

Comments

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

Examples

			First six rows:
1
1....1
3....1....2
9....1....4....4
27...1....6....12...8
81...1....8....24...32...16
		

Crossrefs

Cf. A193788, A038207.

Programs

Mathematica

z = 10; a = 1; b = 2;
p[n_, x_] := (a*x + b)^n
q[n_, x_] := 1 + x^n ; q[n_, 0] := q[n, x] /. x -> 0;
t[n_, k_] := Coefficient[p[n, x], x^k]; t[n_, 0] := p[n, x] /. x -> 0;
w[n_, x_] := Sum[t[n, k]*q[n + 1 - k, x], {k, 0, n}]; w[-1, x_] := 1
g[n_] := CoefficientList[w[n, x], {x}]
TableForm[Table[Reverse[g[n]], {n, -1, z}]]
Flatten[Table[Reverse[g[n]], {n, -1, z}]]  (* A193788 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]]  (* A193789 *)

Formula

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