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A141411
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Defined in comments.
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2
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3, 1, 31, 28, 365, 514, 4388, 8220, 53871, 122284, 673222, 1748055, 8535397, 24383499, 109449848, 334783855, 1415768769, 4548229589, 18434398665, 61345927764, 241210652738, 823296868656, 3167642169823, 11010462627756, 41708741708554, 146886286090602
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| 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).
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REFERENCES
| P. Curtz, Gazette des Mathematiciens, 1992, 52, p.44.
P. Flajolet, X. Gourdon and B. Salvy, Gazette des Mathematiciens, 1993, 55, pp.67-78 .
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MAPLE
| 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);
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CROSSREFS
| See A130620 for another version.
Sequence in context: A188110 A120066 A046979 * A016481 A047815 A095844
Adjacent sequences: A141408 A141409 A141410 * A141412 A141413 A141414
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KEYWORD
| nonn,easy
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AUTHOR
| Paul Curtz (bpcrtz(AT)free.fr), Jun 18 2007
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EXTENSIONS
| 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
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