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A117936 Triangle, rows = inverse binomial transforms of A073133 columns. 2
1, 1, 1, 2, 3, 2, 3, 9, 12, 6, 5, 24, 56, 60, 24, 8, 62, 228, 414, 360, 120 (list; graph; refs; listen; history; internal format)
OFFSET

1,4

COMMENTS

Left border of the triangle = Fibonacci numbers, right border = factorials. Companion triangle A117937 is generated from Lucas polynomials, using analogous operations.

FORMULA

Inverse binomial transforms of A073133 columns. Such columns are f(x), Fibonacci polynomials.

EXAMPLE

First few columns of A073133 are: (1, 1, 1,...); (1, 2, 3,...); (2, 5, 10, 17,...); (3, 12, 33, 72,...). As sequences, these are f(x), Fibonacci polynomials: (1); (x); (x^2 + 1); (x^3 + 2x); (x^4 + 3x^2 + 1); (x^5 + 4x^3 + 3x);...For example, f(x), x = 1,2,3...using (x^4 + 3x^2 + 1) generates Column 5 of A073133: (5, 29, 109, 305...).

Inverse binomial transforms of the foregoing columns generates the triangle rows:

1;

1, 1;

2, 3, 2;

3, 9, 12, 6;

5, 24, 56, 60, 24;

8, 62, 228, 414, 360, 120;

...

CROSSREFS

Cf. A073133, A117937, A117938.

Sequence in context: A085216 A102310 A151546 * A078331 A093868 A194603

Adjacent sequences:  A117933 A117934 A117935 * A117937 A117938 A117939

KEYWORD

nonn

AUTHOR

Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 03 2006

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Last modified February 16 17:48 EST 2012. Contains 205939 sequences.