A140530 Triangle read by rows of coefficients of polynomials defined in comments lines.

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

Offset: 0

Author

Paul Curtz, Jun 04 2007

Keywords

• nonn
• tabl

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.

Crossrefs

A129891 gives the row sums.

Extensions

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