A134261 E.g.f. satisfies: A(x) = x*(sinh(exp(A(x))-1)+1).

0, 1, 2, 9, 68, 735, 10332, 178276, 3639680, 85750461, 2289322710, 68298539441, 2251768422840, 81301875813340, 3190478732975744, 135209859332836905, 6154229137942791184, 299422872446882413387, 15507211446546229257948

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..100

Formula

a(n) ~ n^(n-1) * sqrt(s/(1+exp(2*s)*(s-r))) / (exp(n)*r^n), where r = 0.3186838609215673947... and s = 0.6997097688577272466... are roots of the system of equations s+r*sinh(1-exp(s))=r, exp(s)*r*cosh(1-exp(s))=1. - Vaclav Kotesovec, Jul 16 2014

Maple

A:= proc(n) option remember; if n=0 then 0 else convert (series (x* (sinh (exp(A(n-1))-1)+1), x=0, n+1), polynom) fi end: a:= n-> coeff (A(n), x, n)*n!: seq (a(n), n=0..22);

Mathematica

CoefficientList[InverseSeries[Series[-(x/(-1 + Sinh[1 - E^x])), {x, 0, 20}], x], x] * Range[0, 20]! (* Vaclav Kotesovec, Jul 16 2014 *)

Crossrefs

Sequence in context: A217066 A038037 A138212 * A120980 A020563 A354730

Adjacent sequences: A134258 A134259 A134260 * A134262 A134263 A134264

Keyword

nonn

Author

Alois P. Heinz, Aug 27 2008

Status

approved