A003163 - OEIS

%I M1534 #28 Jan 31 2022 01:19:25

%S 1,2,5,20,350,140,1050,300,57750,38500,250250,45500,2388750,367500,

%T 318750,42500,1088106250,128012500,960093750,101062500,105761906250,

%U 10072562500,2289218750,199062500,8842968750,707437500,51289218750

%N Denominators of Van der Pol numbers.

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

%H T. D. Noe, <a href="/A003163/b003163.txt">Table of n, a(n) for n=0..200</a>

%H F. T. Howard, <a href="https://doi.org/10.1515/crll.1973.260.35">Properties of the van der Pol numbers and polynomials</a>, R. Reine Angew. Math., 260 (1973), 35-46.

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

%e 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

%p 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

%t 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. *)

%Y Cf. A003164.

%K nonn,frac,nice,easy

%O 0,2

%A _N. J. A. Sloane_

%E More terms from _Emeric Deutsch_, Dec 23 2004