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

0,4

Comments

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

Links

Table of n, a(n) for n=0..61.

Formula

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

Example

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

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 *)

Crossrefs

Cf. A193788, A038207.

Sequence in context: A086961 A204003 A085194 * A152252 A152229 A238388

Adjacent sequences: A193786 A193787 A193788 * A193790 A193791 A193792

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 05 2011

Status

approved