1,4

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

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);...

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.

Cf. A117936, A117938.

Sequence in context: A106702 A057435 A050610 this_sequence A110897 A116644 A143050

Adjacent sequences: A117934 A117935 A117936 this_sequence A117938 A117939 A117940

nonn

Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 04 2006