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%I #12 Mar 27 2019 10:01:30
%S 1,0,1,6,29,180,1501,14434,154265,1856232,24953401,368767102,
%T 5936244533,103519338780,1944554725205,39134556793050,840024295910833,
%U 19157944025344464,462629389438242673,11792248121970820598,316398168231432879565,8913743651504295251844
%N Expansion of e.g.f. sec(x*exp(x)).
%e sec(x*exp(x)) = 1 + x^2/2! + 6*x^3/3! + 29*x^4/4! + 180*x^5/5! + 1501*x^6/6! + ...
%p a:=series(sec(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[Sec[x Exp[x]], {x, 0, nmax}], x] Range[0, nmax]!
%t nmax = 21; CoefficientList[Series[1/Cos[x Exp[x]], {x, 0, nmax}], x] Range[0, nmax]!
%Y Cf. A000364, A009007, A009017, A009121, A009300, A009448, A009565, A009635, A009768, A139134, A191719, A216401, A217502, A294313, A297009, A297010.
%K nonn
%O 0,4
%A _Ilya Gutkovskiy_, Dec 27 2017
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