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A190818 Expansion of e.g.f.: 1/(1-2*tanh(x)).

%I A190818 #24 Dec 04 2023 02:44:36
%S A190818 1,2,8,44,320,2912,31808,405344,5903360,96722432,1760811008,
%T A190818 35260703744,770296217600,18229999665152,464622502289408,
%U A190818 12687528814751744,369557965317079040,11437129322496131072,374778854976227115008,12963259774166774841344,471986702056014668103680
%N A190818 Expansion of e.g.f.: 1/(1-2*tanh(x)).
%H A190818 Vincenzo Librandi, <a href="/A190818/b190818.txt">Table of n, a(n) for n = 0..100</a>
%F A190818 E.g.f: 1/(1-2*tanh(x)).
%F A190818 a(n) ~ n! * 2^(n+2)/(3*(log(3))^(n+1)). - _Vaclav Kotesovec_, Jun 26 2013
%p A190818 E(x):=1/(1-2*tanh(x)):
%p A190818 a[0]:=E(x):
%p A190818 for n from 1 to 30 do a[n]:=diff(a[n-1],x) od:
%p A190818 x:=0:
%p A190818 seq(a[n],n=0..30);
%t A190818 CoefficientList[Series[1/(1-2*Tanh[x]), {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Jun 26 2013 *)
%o A190818 (PARI) x='x+O('x^66);
%o A190818 Vec(serlaplace(1/(1-2*tanh(x)))) /* _Joerg Arndt_, May 21 2011 */
%o A190818 (Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!(Laplace( 1/(1-2*Tanh(x)) ))); // _G. C. Greubel_, Dec 03 2023
%o A190818 (SageMath)
%o A190818 def A190818_list(prec):
%o A190818     P.<x> = PowerSeriesRing(QQ, prec)
%o A190818     return P( 1/(1-2*tanh(x)) ).egf_to_ogf().list()
%o A190818 A190818_list(40) # _G. C. Greubel_, Dec 03 2023
%Y A190818 Cf. A011782 (e.g.f. of 1/(1-tanh(x))).
%K A190818 nonn
%O A190818 0,2
%A A190818 _Miklos Kristof_, May 21 2011