A224079 E.g.f. is series reversion of log(1+x)/cosh(x).

1, 1, 4, 25, 191, 1981, 24515, 357393, 6014944, 114374701, 2429126965, 56973837097, 1462548099325, 40790689845725, 1228180553509096, 39706476998683809, 1371869867621426343, 50445615936195883981, 1967026296214873286071, 81070802180747506986681

Offset: 1

Author

Paul D. Hanna, Jul 20 2013

Keywords

• nonn

Examples

			E.g.f.: A(x) = x + x^2/2! + 4*x^3/3! + 25*x^4/4! + 191*x^5/5! + 1981*x^6/6! +...
		

Crossrefs

Cf. A052888.

Programs

Mathematica

Rest[CoefficientList[InverseSeries[Series[Log[1+x]/Cosh[x], {x, 0, 20}], x],x] * Range[0, 20]!] (* Vaclav Kotesovec, Jan 13 2014 *)

PARI

{a(n)=local(X=x+x*O(x^n));n!*polcoeff(serreverse(log(1+X)/cosh(X)), n)}
for(n=1,25,print1(a(n),", "))

Formula

E.g.f. satisfies: 1 + A(x) = exp(x*cosh(A(x))).

a(n) ~ n^(n-1) * ((1+s)*sinh(s))^n * sqrt((1+s)/(1+s+tanh(s))) / exp(n), where s = 0.96996536567590308324... is the root of the equation (1+s)*log(1+s)*tanh(s) = 1. - Vaclav Kotesovec, Jan 13 2014