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A117937 Triangle, rows = inverse binomial transforms of A117938 columns. 3
1, 1, 1, 3, 3, 2, 4, 10, 12, 6, 7, 27, 58, 60, 24, 11, 71, 240, 420, 360, 120 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

A117936 is the companion triangle using analogous Fibonacci polynomials. Left border of A117936 = the Lucas numbers; right border = factorials.

[Note that most of the comments here and in many related sequences by the same author refer to some unusual definition of binomial transforms for sequences starting at index 1. - R. J. Mathar, Jul  05 2012]

LINKS

Table of n, a(n) for n=1..21.

FORMULA

Rows of the triangle are inverse binomial transforms of A117938 columns. A117938 columns are generated from f(x), Lucas polynomials: (1); (x); (x^2 + 2); (x^3 + 3x); (x^4 + 4x + 2);...

EXAMPLE

First few rows of the triangle are:

1;

1, 1;

3, 3, 2;

4, 10, 12, 6;

7, 27, 58, 60, 24;

11, 71, 240, 420, 360, 120;

...

For example, row 4: (4, 10, 12, 6) = the inverse binomial transform of column 4 of A117938: (4, 14, 36, 76, 140...), being f(x), x =1,2,3...using the Lucas polynomial x^3 + 3x.

CROSSREFS

Cf. A117936, A117938.

Sequence in context: A050610 A151848 A238238 * A110897 A116644 A166462

Adjacent sequences:  A117934 A117935 A117936 * A117938 A117939 A117940

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Apr 04 2006

STATUS

approved

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Last modified October 18 18:58 EDT 2018. Contains 316323 sequences. (Running on oeis4.)