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%I #24 Sep 08 2022 08:45:09
%S 1,4,64,1984,97024,6713344,615829504,71654785024,10243143368704,
%T 1755968011239424,354197952894337024,82788022987201183744,
%U 22140953727834378993664,6703959915806302859689984,2277487386474356139699994624,861378969099073547571187154944
%N Expansion of e.g.f.: exp(cosh(2*x)-1), even powers only.
%C Periodic zeros suppressed.
%H Vincenzo Librandi, <a href="/A081559/b081559.txt">Table of n, a(n) for n = 0..100</a>
%F E.g.f.: exp(cosh(2*x))/e = exp(cosh(2*x)-1).
%p seq(coeff(series(exp(cosh(2*x)-1), x, 2*n+1)*factorial(2*n), x, 2*n), n = 0 .. 15); # _G. C. Greubel_, Aug 13 2019
%t With[{nn = 30}, CoefficientList[Series[Exp[Cosh[2*x]-1], {x, 0, nn}], x] Range[0, nn]!][[1 ;; ;; 2]] (* _G. C. Greubel_, Aug 13 2019 *)
%o (PARI) my(x='x+O('x^30)); v=Vec(serlaplace( exp(cosh(2*x)-1) )); vector(#v\2, n, v[2*n-1]) \\ _G. C. Greubel_, Aug 13 2019
%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(Cosh(2*x)-1) )); [Factorial(2*n-2)*b[2*n-1]: n in [1..Floor((m-2)/2)]]; // _G. C. Greubel_, Aug 13 2019
%o (Sage) [factorial(2*n)*( exp(cosh(2*x)-1) ).series(x, 2*n+1).list()[2*n] for n in (0..15)] # _G. C. Greubel_, Aug 13 2019
%Y Cf. A005046, A081560.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Mar 22 2003
%E Definition amended by _Georg Fischer_, Dec 03 2021
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