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Triangle read by rows of coefficients of polynomials defined in comments lines.
1

%I #4 Mar 30 2012 18:51:58

%S 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,

%T 51,55,40,21,7,1

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

%C 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).

%C 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:

%C 1

%C 1 1

%C 1 2 1

%C 2 3 3 1

%C 3 6 6 4 1

%C 4 11 13 10 5 1

%C 5 18 27 24 15 6 1

%C 6 28 51 55 40 21 7 1

%C ...

%C which produces the present sequence.

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

%Y A129891 gives the row sums.

%K nonn,tabl

%O 0,5

%A _Paul Curtz_, Jun 04 2007

%E Edited by _N. J. A. Sloane_, Jul 05 2007