A193900 Mirror of the triangle A193899.

1, 2, 1, 10, 5, 2, 42, 21, 10, 4, 170, 85, 42, 20, 8, 682, 341, 170, 84, 40, 16, 2730, 1365, 682, 340, 168, 80, 32, 10922, 5461, 2730, 1364, 680, 336, 160, 64, 43690, 21845, 10922, 5460, 2728, 1360, 672, 320, 128, 174762, 87381, 43690, 21844, 10920

Offset

0,2

Comments

A193900 is obtained by reversing the rows of the triangle A193899.

Links

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

Formula

Write w(n,k) for the triangle at A193899. The triangle at A193900 is then given by w(n,n-k).

Example

First six rows:
1
2.....1
10....5....2
42....21...10...4
170...85...42...20..8
682...341..170..84..40..16

Mathematica

z = 12;
p[n_, x_] := x*p[n - 1, x] + 2^n; p[0, x_] := 1;
q[n_, x_] := p[n, x];
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}]]  (* A193899 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]]  (* A193900 *)

Crossrefs

Cf. A193899.

Sequence in context: A235608 A112333 A066868 * A319373 A143172 A004747

Adjacent sequences: A193897 A193898 A193899 * A193901 A193902 A193903

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 08 2011

Status

approved