A295278 Expansion of e.g.f. log(1 + x*sech(x))*exp(x).

0, 1, 1, -1, 0, 4, -5, 13, -392, 2112, 7663, -165067, 1011560, -2965756, -11164309, 630876517, -12760548400, 133046910432, -189966787521, -18567623055795, 392188656574896, -5061972266268844, 33655544331988203, 565132153437469165, -26647451471277927416

Offset: 0

Author

Ilya Gutkovskiy, Dec 27 2017

Keywords

• sign

Examples

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

Crossrefs

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

Programs

Maple

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

Mathematica

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