login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A129891 Sum of coefficients of polynomials defined in comments lines. 6
1, 2, 4, 9, 20, 44, 96, 209, 455, 991, 2159, 4704, 10249, 22330, 48651, 105997, 230938, 503150, 1096225, 2388372, 5203604, 11337218, 24700671, 53815949, 117250109, 255455647, 556567394, 1212606837, 2641935832, 5756049469, 12540844137 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

At the same time that I introduced the polynomials P(n,x) defined by P(0,x)=1 and for n>0, P(n,x)=((-1)^n)/(n+1) + x*Sum_{ i=0..n-1 } [(((-1)^i)/(i+1))*P(n-1-i,x)] (Gazette des Mathematiciens 1992), I gave the generalization P(0,x)=u(0), P(n,x) = u(n) + x*Sum_{ i=0..n-1 } u(i)*P(n-1-i,x).

For u(n), n>=0, = 1 1 1 2 3 4 5 6 7 8 ... the array of coefficients of the polynomials P(n,x) is:

1

1 1

1 2 1

2 3 3 1

3 6 6 4 1

4 11 13 10 5 1

5 18 27 24 15 6 1

6 28 51 55 40 21 7 1

whose row sums are the present sequence.

The alternating row sums are 1 0 0 1 0 0 0 -1 ...

The antidiagonal sums are 1 1 2 4 7 13 23 41 73 ...

The first column of the inverse matrix is 1 -1 1 -2 5 -11 25 -63 ...

REFERENCES

P. Curtz, Gazette des Mathematiciens, 1992, no. 52, p. 44.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

FORMULA

G.f.: -(x^3-x+1)/(x^4-2*x^2+3*x-1). - Alois P. Heinz, Oct 14 2009

MAPLE

a:= n-> (Matrix([1, 1, 0, 1]). Matrix(4, (i, j)-> if i=j-1 then 1 elif j=1 then [3, -2, 0, 1][i] else 0 fi)^n)[1, 1]:

seq(a(n), n=0..50);  # Alois P. Heinz, Oct 14 2009

MATHEMATICA

ClearAll[u, p]; u[n_ /; n < 3] = 1; u[n_] := n-1; p[0][x_] := u[0]; p[n_][x_] := p[n][x] = u[n] + x*Sum[ u[i]*p[n-i-1][x] , {i, 0, n-1}] // Expand; row[n_] := CoefficientList[ p[n][x], x]; Table[row[n] // Total, {n, 0, 30}] (* Jean-Fran├žois Alcover, Oct 02 2012 *)

CROSSREFS

Sums of coefficients of polynomials defined in A140530.

Cf. A129841, A129696, A130620.

Sequence in context: A266930 A034007 A109975 * A130587 A129988 A035530

Adjacent sequences:  A129888 A129889 A129890 * A129892 A129893 A129894

KEYWORD

nonn

AUTHOR

Paul Curtz, Jun 04 2007

EXTENSIONS

Edited by N. J. A. Sloane, Jul 05 2007

More terms from Alois P. Heinz, Oct 14 2009

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 August 18 01:19 EDT 2019. Contains 326059 sequences. (Running on oeis4.)