A193799 Mirror of the triangle A193798.

1, 1, 1, 5, 3, 2, 25, 9, 12, 4, 125, 27, 54, 36, 8, 625, 81, 216, 216, 96, 16, 3125, 243, 810, 1080, 720, 240, 32, 15625, 729, 2916, 4860, 4320, 2160, 576, 64, 78125, 2187, 10206, 20412, 22680, 15120, 6048, 1344, 128, 390625, 6561, 34992, 81648, 108864

Offset

0,4

Comments

A193799 is obtained by reversing the rows of the triangle A193798.

Links

Table of n, a(n) for n=0..49.

Formula

Write w(n,k) for the triangle at A193798. The triangle at A193799 is then given by w(n,n-k).

Example

First six rows:
1
1.....1
5.....3....2
25....9....12....4
125...27...54....36...8
625...81...216...216..96..16

Mathematica

z = 8; a = 3; 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}]]  (* A193798 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]]  (* A193799 *)

Crossrefs

Cf. A193798.

Sequence in context: A322289 A259228 A241182 * A262225 A330092 A064812

Adjacent sequences: A193796 A193797 A193798 * A193800 A193801 A193802

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 05 2011

Status

approved