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A140530 Triangle read by rows of coefficients of polynomials defined in comments lines. 1
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

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

...

which produces the present sequence.

REFERENCES

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

LINKS

Table of n, a(n) for n=0..35.

CROSSREFS

A129891 gives the row sums.

Sequence in context: A057041 A267177 A099567 * A202191 A052250 A099569

Adjacent sequences:  A140527 A140528 A140529 * A140531 A140532 A140533

KEYWORD

nonn,tabl

AUTHOR

Paul Curtz, Jun 04 2007

EXTENSIONS

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

STATUS

approved

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Last modified April 19 20:51 EDT 2019. Contains 322291 sequences. (Running on oeis4.)