A295278 - OEIS

%I #28 Mar 27 2019 10:02:49

%S 0,1,1,-1,0,4,-5,13,-392,2112,7663,-165067,1011560,-2965756,-11164309,

%T 630876517,-12760548400,133046910432,-189966787521,-18567623055795,

%U 392188656574896,-5061972266268844,33655544331988203,565132153437469165,-26647451471277927416

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

%e log(1 + x*sech(x))*exp(x) = x/1! + x^2/2! - x^3/3! + 4*x^5/5! - 5*x^6/6! + ...

%p a:=series(log(1+x*sech(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 Sech[x]] Exp[x], {x, 0, nmax}], x] Range[0, nmax]!

%Y Cf. A009353, A009390, A009443, A009843, A294314, A296336, A296437, A296439, A297206.

%K sign

%O 0,6

%A _Ilya Gutkovskiy_, Dec 27 2017