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A003163 Denominators of Van der Pol numbers.
(Formerly M1534)
2
1, 2, 5, 20, 350, 140, 1050, 300, 57750, 38500, 250250, 45500, 2388750, 367500, 318750, 42500, 1088106250, 128012500, 960093750, 101062500, 105761906250, 10072562500, 2289218750, 199062500, 8842968750, 707437500, 51289218750 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

F. T. Howard, Properties of the van der Pol numbers and polynomials, R. Reine Angew. Math., 260 (1973), 35-46.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

T. D. Noe, Table of n, a(n) for n=0..200

FORMULA

E.g.f.: x^3/( 6*x*(exp(x)+1)-12*(exp(x)-1) ).

EXAMPLE

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

MAPLE

G:=x^3/(6*x*(exp(x)+1)-12*(exp(x)-1)):Gser:=series(G, x=0, 35):1, seq(denom(n!*coeff(Gser, x^n)), n=1..31); (Deutsch)

MATHEMATICA

max = 26; g[x_] = x^3/(6*x*(E^x + 1) - 12*(E^x - 1)); Denominator[ CoefficientList[ Series[ g[x], {x, 0, max}], x]*Range[0, max]!](* Jean-Fran├žois Alcover, Nov 17 2011, after g.f. *)

CROSSREFS

Cf. A003164.

Sequence in context: A158872 A216462 A006893 * A088498 A240147 A293687

Adjacent sequences:  A003160 A003161 A003162 * A003164 A003165 A003166

KEYWORD

nonn,frac,nice,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Emeric Deutsch, Dec 23 2004

STATUS

approved

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Last modified January 16 06:59 EST 2019. Contains 319188 sequences. (Running on oeis4.)