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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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified August 17 11:06 EDT 2019. Contains 326057 sequences. (Running on oeis4.)