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A193851 Mirror of the triangle A193850. 4
2, 8, 4, 26, 20, 8, 80, 72, 48, 16, 242, 232, 192, 112, 32, 728, 716, 656, 496, 256, 64, 2186, 2172, 2088, 1808, 1248, 576, 128, 6560, 6544, 6432, 5984, 4864, 3072, 1280, 256, 19682, 19664, 19520, 18848, 16832, 12800, 7424, 2816, 512, 59048, 59028 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

A193851 is obtained by reversing the rows of the triangle A193850.

LINKS

Table of n, a(n) for n=0..46.

FORMULA

Write w(n,k) for the triangle at A193850.  The triangle at A193851 is then given by w(n,n-k).

EXAMPLE

First six rows:

2

8....4

26...20....8

80...72...40..16

242...232...192...112...32

728...716...656...496..256..64

MATHEMATICA

z = 10;

p[n_, x_] := (x + 2)^n;

q[0, x_] := 1; q[n_, x_] := x*q[n - 1, x] + 1;

p1[n_, k_] := Coefficient[p[n, x], x^k];

p1[n_, 0] := p[n, x] /. x -> 0;

d[n_, x_] := Sum[p1[n, k]*q[n - 1 - k, x], {k, 0, n - 1}]

h[n_] := CoefficientList[d[n, x], {x}]

TableForm[Table[Reverse[h[n]], {n, 0, z}]]

Flatten[Table[Reverse[h[n]], {n, -1, z}]]  (* A193850 *)

TableForm[Table[h[n], {n, 0, z}]]

Flatten[Table[h[n], {n, -1, z}]]   (* A193851  *)

TableForm[Table[Reverse[h[n]/2], {n, 0, z}]]

Flatten[Table[Reverse[h[n]]/2, {n, -1, z}]] (* A193852 *)

TableForm[Table[h[n]/2, {n, 0, z}]]

Flatten[Table[h[n]/2, {n, -1, z}]]  (* A193853 *)

CROSSREFS

Cf. A193850, A193853.

Sequence in context: A019193 A253884 A054788 * A276624 A193847 A019194

Adjacent sequences:  A193848 A193849 A193850 * A193852 A193853 A193854

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 07 2011

STATUS

approved

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Last modified October 27 12:04 EDT 2021. Contains 348276 sequences. (Running on oeis4.)