login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A117937 Triangle, rows = inverse binomial transforms of A117938 columns. 4
1, 1, 1, 3, 3, 2, 4, 10, 12, 6, 7, 27, 58, 60, 24, 11, 71, 240, 420, 360, 120, 18, 180, 920, 2460, 3504, 2520, 720, 29, 449, 3360, 13020, 27720, 32760, 20160, 5040, 47, 1107, 11898, 64620, 194184, 337680, 338400, 181440, 40320, 76, 2710, 41268, 307194, 1257120, 3029760, 4415040 (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..52.

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.

MAPLE

A117937 := proc(n, k)

    add( A117938(n+i, n)*binomial(k-1, i)*(-1)^(1+i-k), i=0..k-1) ;

end proc:

seq(seq(A117937(n, k), k=1..n), n=1..13) ; # R. J. Mathar, Aug 16 2019

CROSSREFS

Cf. A117936, A117938.

Sequence in context: A050610 A151848 A238238 * A110897 A116644 A166462

Adjacent sequences:  A117934 A117935 A117936 * A117938 A117939 A117940

KEYWORD

nonn,tabl,easy

AUTHOR

Gary W. Adamson, Apr 04 2006

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 07:59 EDT 2020. Contains 333079 sequences. (Running on oeis4.)