%I #8 Mar 27 2019 03:50:44

%S 0,1,1,5,0,44,-245,1917,-17976,191760,-2268017,29862645,-432485152,

%T 6819543964,-116400819509,2138673633397,-42078450265744,

%U 882702459984256,-19667723002057473,463866294631620941,-11545312970532620104,302416006623761207804,-8316019118849688156693

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

%e log(1 + x*cosh(x))*exp(x) = x/1! + x^2/2! + 5*x^3/3! + 44*x^5/5! - 245*x^6/6! + ...

%p a:=series(log(1 + x*cosh(x))*exp(x),x=0,23): seq(n!*coeff(a,x,n),n=0..22); # _Paolo P. Lava_, Mar 26 2019

%t nmax = 22; CoefficientList[Series[Log[1 + x Cosh[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*cosh(x))))) \\ _Altug Alkan_, Dec 28 2017

%Y Cf. A009305, A009353, A009390, A294314, A295278, A296336, A296437, A296439.

%K sign

%O 0,4

%A _Ilya Gutkovskiy_, Dec 27 2017