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%I #12 Sep 08 2022 08:45:09
%S 1,1,2,4,11,31,107,379,1556,6556,31007,150349,801341,4373461,25853102,
%T 156297964,1012382291,6698486371,47089993967,337789490599,
%U 2557480572656,19738202807236,159928950077327,1319703681935929,11382338060040761,99896787342523081
%N Binomial transform of expansion of exp(cosh(x)), A005046.
%H Vincenzo Librandi, <a href="/A081557/b081557.txt">Table of n, a(n) for n = 0..200</a>
%F E.g.f.: exp(x) * exp(cosh(x)) / e = exp(cosh(x)+x-1).
%p seq(coeff(series(exp(cosh(x)+x-1), x, n+1)*factorial(n), x, n), n = 0 .. 30); # _G. C. Greubel_, Aug 13 2019
%t With[{nn = 30}, CoefficientList[Series[Exp[Cosh[x] + x - 1], {x, 0, nn}], x] Range[0, nn]!] (* _Vincenzo Librandi_, Aug 08 2013 *)
%o (PARI) my(x='x+O('x^30)); Vec(serlaplace( exp(cosh(x)+x-1) )) \\ _G. C. Greubel_, Aug 13 2019
%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(Cosh(x)+x-1) )); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, Aug 13 2019
%o (Sage) [factorial(n)*( exp(cosh(x)+x-1) ).series(x,n+1).list()[n] for n in (0..30)] # _G. C. Greubel_, Aug 13 2019
%Y Cf. A081558.
%K easy,nonn
%O 0,3
%A _Paul Barry_, Mar 22 2003
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