%I #18 Mar 27 2019 10:03:50

%S 0,1,1,-1,0,-16,-5,13,-1512,12336,-98177,444773,1249160,-75244508,

%T 1296229779,-15956614403,130892534160,59122803744,-31478991643617,

%U 837166840532589,-14900078660739984,181343532181629332,-480411914937891389,-54306065912649098539,2080183542455901881320

%N Expansion of e.g.f. log(1 + x*cos(x))*exp(x).

%e log(1 + x*cos(x))*exp(x) = x/1! + x^2/2! - x^3/3! - 16*x^5/5! - 5*x^6/6! + ...

%p a:=series(log(1 + x*cos(x))*exp(x),x=0,25): seq(n!*coeff(a,x,n),n=0..24); # _Paolo P. Lava_, Mar 27 2019

%t nmax = 24; CoefficientList[Series[Log[1 + x Cos[x]] Exp[x], {x, 0, nmax}], x] Range[0, nmax]!

%o (PARI) x='x+O('x^99); concat([0], Vec(serlaplace(exp(x)*log(1+x*cos(x))))) \\ _Altug Alkan_, Dec 28 2017

%Y Cf. A003728, A009334, A009371, A294314, A295278, A296436, A296438, A297206.

%K sign

%O 0,6

%A _Ilya Gutkovskiy_, Dec 27 2017