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%I #10 Mar 27 2019 10:01:45
%S 0,1,1,5,0,64,-245,2757,-23576,272256,-3270977,45055845,-671589952,
%T 10984688636,-193875825117,3688182769117,-75085512079184,
%U 1630385857436224,-37596306847103457,917765946045581357,-23641953753495247624,640958728426947233468,-18242640219843554954221
%N Expansion of e.g.f. log(1 + x*sec(x))*exp(x).
%e log(1 + x*sec(x))*exp(x) = x/1! + x^2/2! + 5*x^3/3! + 64*x^5/5! - 245*x^6/6! + ...
%p a:=series(log(1+x*sec(x))*exp(x),x=0,23): seq(n!*coeff(a,x,n),n=0..22); # _Paolo P. Lava_, Mar 27 2019
%t nmax = 22; CoefficientList[Series[Log[1 + x Sec[x]] Exp[x], {x, 0, nmax}], x] Range[0, nmax]!
%Y Cf. A009334, A009371, A009442, A009843, A295278, A296336, A296436, A296438, A297206.
%K sign
%O 0,4
%A _Ilya Gutkovskiy_, Dec 27 2017