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%I #13 Sep 08 2022 08:45:24
%S 1,1,5,13,105,441,5165,30213,469585,3529201,68525525,629401213,
%T 14664091065,159175688361,4326609913085,54189700721013,
%U 1683369010256545,23894940183997921,835066388382183845,13248060325188261613
%N Expansion of e.g.f.: exp(x)*sec(2*x).
%C Row sums of A117436.
%C Binomial transform of A002436 (with interpolated zeros).
%H G. C. Greubel, <a href="/A117437/b117437.txt">Table of n, a(n) for n = 0..425</a>
%F a(n) ~ n! * 2^(2*n+1) * (exp(Pi/4) + (-1)^n*exp(-Pi/4)) / Pi^(n+1). - _Vaclav Kotesovec_, Aug 04 2014
%t With[{nn=30},CoefficientList[Series[Exp[x]Sec[2x],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Dec 13 2011 *)
%o (Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!(Laplace( Exp(x)*Sec(2*x) ))); // _G. C. Greubel_, May 31 2021
%o (Sage) [factorial(n)*( exp(x)*sec(2*x) ).series(x,n+1).list()[n] for n in (0..30)] # _G. C. Greubel_, May 31 2021
%o (PARI) my(x='x+O('x^30)); Vec(serlaplace(exp(x)/cos(2*x))) \\ _Michel Marcus_, Jun 01 2021
%Y Cf. A002436, A117436.
%K easy,nonn
%O 0,3
%A _Paul Barry_, Mar 16 2006
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