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%I #36 May 12 2024 17:44:33
%S 0,1,2,5,12,41,142,685,3192,19921,116282,887765,6219972,56126201,
%T 458790022,4776869245,44625674352,526589630881,5534347077362,
%U 72989204937125,852334810990332,12424192360405961,159592488559874302,2547879762929443405,35703580441464231912
%N E.g.f. tan(x)*exp(x).
%H Robert Israel, <a href="/A009739/b009739.txt">Table of n, a(n) for n = 0..484</a>
%F a(2n) = A009747(n), a(2n+1) = A003719(n).
%F E.g.f.: exp(x)*tan(x). - _Zerinvary Lajos_, Apr 05 2009
%F G.f.: 1/(x-1)/Q(0), where Q(k)= 1 - 1/x - (k+1)*(k+2)/Q(k+1); (continued fraction). - _Sergei N. Gladkovskii_, Apr 26 2013
%F G.f.: x/(1-x)/Q(0), where Q(k)= 1 - x - x^2*(k+1)*(k+2)/Q(k+1); (continued fraction). - _Sergei N. Gladkovskii_, Apr 26 2013
%F G.f.: G(0)*x/(1-x)^2, where G(k) = 1 - x^2*(k+1)*(k+2)/(x^2*(k+1)*(k+2) - (1-x)^2/G(k+1) ); (continued fraction). - _Sergei N. Gladkovskii_, Jan 23 2014
%F a(n) ~ 2^(3/2 + n)*(exp(Pi) - (-1)^n)*exp(-Pi/2 - n)*Pi^(-1/2 - n)*n^(1/2 + n). - _Robert Israel_, Sep 22 2019
%p G(x):=exp(x)*tan(x): f[0]:=G(x): for n from 1 to 54 do f[n]:=diff(f[n-1],x) od: x:=0: seq(f[n],n=0..22 ); # _Zerinvary Lajos_, Apr 05 2009
%p # Alternative:
%p S:= series(exp(x)*tan(x),x, 51):
%p seq(coeff(S,x,j)*j!,j=0..50); # _Robert Israel_, Sep 22 2019
%o (PARI) x='x+O('x^66); concat([0],Vec(serlaplace(tan(x)*exp(x)))) \\ _Joerg Arndt_, Apr 26 2013
%Y Cf. A003701.
%K nonn,easy
%O 0,3
%A _R. H. Hardin_
%E Extended and signs tested by _Olivier Gérard_, Mar 15 1997
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