

A193900


Mirror of the triangle A193899.


2



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
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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,nk).


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



