A193920 - OEIS

A193920

Mirror of the triangle A193919.

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

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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

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