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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
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
A129891 gives the row sums.
Sequence in context: A057041 A267177 A099567 * A202191 A052250 A333878
KEYWORD
nonn,tabl
AUTHOR
Paul Curtz, Jun 04 2007
EXTENSIONS
Edited by N. J. A. Sloane, Jul 05 2007
STATUS
approved