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A193920 Mirror of the triangle A193919. 2
1, 1, 1, 2, 3, 1, 4, 9, 7, 2, 7, 21, 25, 14, 3, 12, 46, 75, 64, 28, 5, 20, 94, 195, 224, 148, 53, 8, 33, 185, 468, 679, 603, 326, 99, 13, 54, 353, 1056, 1855, 2073, 1502, 687, 181, 21, 88, 659, 2280, 4711, 6357, 5786, 3543, 1405, 327, 34, 143, 1209, 4755 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

A193920 is obtained by reversing the rows of the triangle A193919.

LINKS

Table of n, a(n) for n=0..57.

FORMULA

Write w(n,k) for the triangle at A193919.  The triangle at A193920 is then given by w(n,n-k).

EXAMPLE

First six rows:

1

1....1

2....3....1

4....9....7....2

7....21...25...14...3

12...46...75...64...28...5

MATHEMATICA

p[n_, x_] := Sum[Fibonacci[k + 1]*x^(n - k), {k, 0, n}];

q[n_, x_] := (x + 1)^n;

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}]]  (* A193919 *)

TableForm[Table[g[n], {n, -1, z}]]

Flatten[Table[g[n], {n, -1, z}]]  (* A193920 *)

CROSSREFS

Cf. A193919.

Sequence in context: A165241 A119865 A177896 * A076732 A130152 A211233

Adjacent sequences:  A193917 A193918 A193919 * A193921 A193922 A193923

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 09 2011

STATUS

approved

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Last modified April 7 18:53 EDT 2020. Contains 333306 sequences. (Running on oeis4.)