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%I #22 Sep 08 2022 08:44:37
%S 1,0,-1,-6,-27,-100,-237,742,18025,194904,1689671,12483570,72272013,
%T 155614004,-4305757029,-101460169442,-1561477983407,-20064006763728,
%U -223375429298929,-2048612121431958,-11401251676320843,95849085744834380
%N Expansion of e.g.f. cos(sinh(x)*exp(x)).
%H G. C. Greubel, <a href="/A009061/b009061.txt">Table of n, a(n) for n = 0..250</a>
%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/BellPolynomial.html">Bell Polynomial</a>.
%F a(n) = 2^n*Re(B_n(i/2)), where B_n(x) is n-th Bell polynomial, i=sqrt(-1). _Vladimir Reshetnikov_, Oct 22 2015
%p seq(coeff(series(factorial(n)*cos(sinh(x)*exp(x)), x,n+1),x,n),n=0..25); # _Muniru A Asiru_, Jul 24 2018
%t Table[SeriesCoefficient[Cos[Sinh[x] Exp[x]], {x, 0, n}] n!, {n, 0, 20}]
%t Table[2^n Re[BellB[n, I/2]], {n, 0, 20}] (* _Vladimir Reshetnikov_, Oct 22 2015 *)
%o (PARI) x='x+O('x^30); Vec(serlaplace(cos(sinh(x)*exp(x)))) \\ _G. C. Greubel_, Jul 23 2018
%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Cos(Sinh(x)*Exp(x)))); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, Jul 23 2018
%Y Cf. A009496, A121868.
%K sign,easy
%O 0,4
%A _R. H. Hardin_
%E Extended with signs by _Olivier Gérard_, Mar 15 1997
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