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A003164
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Numerators of Van der Pol numbers.
(Formerly M5262)
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2
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1, -1, 1, -1, -1, 1, 1, -1, -37, 111, 177, -177, -2753, 2753, 827, -827, -8386459, 8386459, 28033727, -28033727, -14529522883, 14529522883, 1799010587, -1799010587, -47497385017, 47497385017, 2217167083651, -19954503752859
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OFFSET
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0,9
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COMMENTS
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Named after the Dutch physicist Balthasar van der Pol (1889-1959). - Amiram Eldar, Sep 04 2021
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
B. van der Pol, Smoothing and "unsmoothing", in Mark Kac, Probability and Related Topics in Physical Sciences, New York 1957, pp. 223—235.
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LINKS
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FORMULA
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E.g.f. for fractions: x^3/( 6*x*(exp(x)+1)-12*(exp(x)-1) ).
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EXAMPLE
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1, -1/2, 1/5, -1/20, -1/350, 1/140, 1/1050, -1/300, -37/57750, 111/38500, 177/250250, -177/45500, ... = A003163/A003164.
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MATHEMATICA
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max = 27; g[x_] = x^3/(6*x*(E^x + 1) - 12*(E^x - 1)); Numerator[ CoefficientList[ Series[ g[x], {x, 0, max}], x]*Range[0, max]!](* Jean-François Alcover, Nov 17 2011, after g.f. *)
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CROSSREFS
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KEYWORD
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sign,frac,nice
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AUTHOR
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STATUS
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approved
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