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

0,4

Comments

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

Links

Table of n, a(n) for n=0..60.

Formula

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

Example

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

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 *)

Crossrefs

Cf. A193790.

Sequence in context: A079749 A156647 A183154 * A160760 A152860 A002350

Adjacent sequences: A193788 A193789 A193790 * A193792 A193793 A193794

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 05 2011

Status

approved