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%I #10 Mar 27 2019 10:01:37
%S 1,0,-1,-6,-19,20,899,7966,27705,-366552,-8374201,-80690302,9794597,
%T 16015845820,317370642315,2554368906150,-37571987331343,
%U -1784464543440304,-31315944840101233,-80221319702865398,12685422355781995485,422083364962616527716
%N Expansion of e.g.f. sech(x*exp(x)).
%e sech(x*exp(x)) = 1 - x^2/2! - 6*x^3/3! - 19*x^4/4! + 20*x^5/5! + 899*x^6/6! + ...
%p a:=series(sech(x*exp(x)),x=0,22): seq(n!*coeff(a,x,n),n=0..21); # _Paolo P. Lava_, Mar 27 2019
%t nmax = 21; CoefficientList[Series[Sech[x Exp[x]], {x, 0, nmax}], x] Range[0, nmax]!
%t nmax = 21; CoefficientList[Series[1/Cosh[x Exp[x]], {x, 0, nmax}], x] Range[0, nmax]!
%Y Cf. A000364, A009017, A009121, A009301, A009448, A009565, A009635, A009768, A191719, A216401, A217502, A294312, A296544, A297009, A297010.
%K sign
%O 0,4
%A _Ilya Gutkovskiy_, Dec 27 2017