0,1

Given any sequence {u(i), i >= 0} we define a family of polynomials by P(0,x) = u(0), P(n,x) = u(n) + x*Sum_{ i=0..n-1 } (u(i)*P(n-i-1, x). Then we set a(n) = (P(n,-1)+P(n,1))/2.

For the present exanmple we take {u(i)} to be 3,1,4,1,5,9,... (A000796).

P. Curtz, Gazette des Mathematiciens, 1992, 52, p.44.

P. Flajolet, X. Gourdon and B. Salvy, Gazette des Mathematiciens, 1993, 55, pp.67-78 .

u:= proc(n) Digits:= max(n+10);

trunc (10* frac (evalf (Pi*10^(n-1))))

end:

P:= proc(n) option remember; local i, x;

if n=0 then u(0)

else unapply

(expand (u(n) +x *add (u(i) *P(n-i-1)(x), i=0..n-1)), x)

fi

end:

a:= n-> (P(n)(1)+P(n)(-1))/2:

seq (a(n), n=0..30);

See A130620 for another version.

Sequence in context: A165624 A120066 A046979 this_sequence A016481 A047815 A095844

Adjacent sequences: A141408 A141409 A141410 this_sequence A141412 A141413 A141414

nonn,easy

Paul Curtz (bpcrtz(AT)free.fr), Jun 18 2007

Edited by N. J. A. Sloane, Aug 26 2009

Corrected and extended with Maple program by Alois Heinz (heinz(AT)hs-heilbronn.de), Sep 06 2009