login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A003164 Numerators of Van der Pol numbers.
(Formerly M5262)
2

%I M5262 #27 Jan 31 2022 01:19:47

%S 1,-1,1,-1,-1,1,1,-1,-37,111,177,-177,-2753,2753,827,-827,-8386459,

%T 8386459,28033727,-28033727,-14529522883,14529522883,1799010587,

%U -1799010587,-47497385017,47497385017,2217167083651,-19954503752859

%N Numerators of Van der Pol numbers.

%C Named after the Dutch physicist Balthasar van der Pol (1889-1959). - _Amiram Eldar_, Sep 04 2021

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

%D B. van der Pol, Smoothing and "unsmoothing", in Mark Kac, Probability and Related Topics in Physical Sciences, New York 1957, pp. 223—235.

%H T. D. Noe, <a href="/A003164/b003164.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), pp. 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.

%t 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. *)

%Y Cf. A003163 (denominators).

%K sign,frac,nice

%O 0,9

%A _N. J. A. Sloane_

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)