A193851 Mirror of the triangle A193850.

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

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: A369178 A253884 A054788 * A276624 A193847 A019194

Adjacent sequences: A193848 A193849 A193850 * A193852 A193853 A193854

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 07 2011

Status

approved