A133359 E.g.f. satisfies: A(x) = x*(cosh(exp(A(x))-1)).

0, 1, 0, 3, 12, 100, 1050, 12649, 185752, 3112407, 59052390, 1252912584, 29341892580, 752441547741, 20966217326418, 630757511101995, 20377626191365936, 703606826009437384, 25858057389119292222

Offset

0,4

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)) / (exp(n) * r^n), where r = 0.4494712387490528668... and s = 0.6780159617201756415... are roots of the system of equations 1+exp(s)*r*sinh(1-exp(s)) = 0, s = r*cosh(1-exp(s)). - Vaclav Kotesovec, Jul 16 2014

Maple

A:= proc(n) option remember; if n=0 then 0 else convert (series (x* (cosh (exp(A(n-1))-1)), x=0, n+1), polynom) fi end: a:= n-> coeff (A(n), x, n)*n!: seq (a(n), n=0..24);

Mathematica

A[n_] := A[n] = If[n == 0, 0, Normal[Series[x*(Cosh[Exp[A[n-1]]-1]), {x, 0, n+1}]]]; a[n_] := Coefficient[A[n], x, n]*n!; Table[a[n], {n, 0, 24}] (* Jean-François Alcover, Mar 05 2014, after Alois P. Heinz *)
CoefficientList[InverseSeries[Series[x*Sech[1 - E^x], {x, 0, 20}], x], x] * Range[0, 20]! (* Vaclav Kotesovec, Jul 16 2014 *)

Crossrefs

Sequence in context: A374582 A162055 A067300 * A102687 A202302 A350953

Adjacent sequences: A133356 A133357 A133358 * A133360 A133361 A133362

Keyword

nonn

Author

Alois P. Heinz, Aug 27 2008

Status

approved