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A192238
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Constant term in the reduction of the polynomial x(x+1)(x+2)...(x+n-1) by x^2 -> x+1.
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3
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1, 0, 1, 6, 37, 256, 1999, 17490, 169895, 1816320, 21205745, 268547510, 3667187645, 53722014720, 840455448415, 13985762375970, 246675543859855, 4596826887347200, 90249727067243425, 1861971659969854950, 40274219840308939925
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OFFSET
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1,4
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COMMENTS
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LINKS
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FORMULA
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Conjecture: a(n) +2*(-n+1)*a(n-1) +(n^2-3*n+1)*a(n-2)=0. - R. J. Mathar, May 04 2014
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MATHEMATICA
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q[x_] := x + 1;
p[0, x_] := 1; p[1, x_] := x;
p[n_, x_] := (x + n) p[n - 1, x] /; n > 1
reductionRules = {x^y_?EvenQ -> q[x]^(y/2),
x^y_?OddQ -> x q[x]^((y - 1)/2)};
t = Table[
Last[Most[
FixedPointList[Expand[#1 /. reductionRules] &, p[n, x]]]], {n, 0,
20}]
Table[Coefficient[Part[t, n], x, 0], {n, 1, 20}] (* A192238 *)
Table[Coefficient[Part[t, n], x, 1], {n, 1, 20}] (* A192239 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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