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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

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

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

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); # Emeric Deutsch, Dec 23 2004

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: A308522 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 October 16 13:51 EDT 2019. Contains 328093 sequences. (Running on oeis4.)