A193791 Mirror of the triangle A193790.

1, 1, 1, 3, 2, 1, 9, 4, 4, 1, 27, 8, 12, 6, 1, 81, 16, 32, 24, 8, 1, 243, 32, 80, 80, 40, 10, 1, 729, 64, 192, 240, 160, 60, 12, 1, 2187, 128, 448, 672, 560, 280, 84, 14, 1, 6561, 256, 1024, 1792, 1792, 1120, 448, 112, 16, 1, 19683, 512, 2304, 4608, 5376, 4032

Offset: 0

Author

Clark Kimberling, Aug 05 2011

Keywords

• nonn
• tabl

Comments

A193791 is obtained by reversing the rows of the triangle A193790.

Examples

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

Crossrefs

Cf. A193790.

Programs

Mathematica

z = 10; a = 2; b = 1;
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}]]  (* A193790 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]]  (* A193791 *)

Formula

Write w(n,k) for the triangle at A193790. The triangle at A193791 is then given by w(n,n-k).