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.
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Paul Curtz, Jun 04 2007
EXTENSIONS
Edited by N. J. A. Sloane, Jul 05 2007
STATUS
approved