A003163 Denominators of Van der Pol numbers. (Formerly M1534)

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

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. for fractions: 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-François Alcover, Nov 17 2011, after g.f. *)

Crossrefs

Cf. A003164.

Sequence in context: A308522 A216462 A006893 * A088498 A240147 A358556

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