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A192745
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Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined below in Comments.
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2
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0, 1, 2, 5, 13, 42, 175, 937, 6152, 47409, 416441, 4092650, 44425891, 527520141, 6798966832, 94504778173, 1408978113005, 22426272779178, 379522678988183, 6804322657495361, 128828945745315544, 2568535276579450905, 53788306394034206449
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OFFSET
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0,3
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COMMENTS
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The titular polynomial is defined recursively by p(n,x)=x*(n-1,x)+n! for n>0, where p(0,x)=1. For discussions of polynomial reduction, see A192232 and A192744.
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LINKS
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Table of n, a(n) for n=0..22.
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FORMULA
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G.f.: x/(1-x-x^2)/Q(0), where Q(k)= 1 - x*(k+1)/(1 - x*(k+1)/Q(k+1)); (continued fraction). - Sergei N. Gladkovskii, May 20 2013
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EXAMPLE
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The first six polynomials and their reductions are shown here:
1 -> 1
1+x -> 1+x
2+x+x^2 -> 3+2x
6+2x+x^2+x^3 -> 8+5x
24+6x+2x^2+x^4+x^5 -> 29+13x
From those, read A192744=(1,1,3,8,29,...) and A192745=(0,1,2,5,13,...).
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MATHEMATICA
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(See A192744.)
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CROSSREFS
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A192744, A192232.
Sequence in context: A149874 A114297 A178682 * A212824 A119533 A066740
Adjacent sequences: A192742 A192743 A192744 * A192746 A192747 A192748
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KEYWORD
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nonn,changed
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AUTHOR
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Clark Kimberling, Jul 09 2011
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STATUS
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approved
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