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A193799 Mirror of the triangle A193798. 2
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 (list; table; graph; refs; listen; history; text; internal format)
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: A193958 A259228 A241182 * A262225 A064812 A282469

Adjacent sequences:  A193796 A193797 A193798 * A193800 A193801 A193802

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 05 2011

STATUS

approved

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Last modified February 24 15:37 EST 2018. Contains 299623 sequences. (Running on oeis4.)