0,5

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.

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

A129891 gives the row sums.

Sequence in context: A100002 A057041 A099567 this_sequence A052250 A099569 A097724

Adjacent sequences: A140527 A140528 A140529 this_sequence A140531 A140532 A140533

nonn,tabl

Paul Curtz (bpcrtz(AT)free.fr), Jun 04 2007

Edited by N. J. A. Sloane (njas(AT)research.att.com), Jul 05 2007