A133553 E.g.f. satisfies: A(x) = x*(sec(exp(A(x))-1)).

0, 1, 0, 3, 12, 120, 1290, 17409, 277592, 5083659, 105675030, 2452220144, 62891640900, 1766131052829, 53900956145218, 1776400037307315, 62874491729108656, 2378684861565934468, 95790461019732936558

Offset

0,4

Links

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

Formula

a(n) ~ n^(n-1) * s / (exp(n) * r^n * sqrt(1+s+(exp(2*s)*s^4)/r^2)), where r = 0.4099354376925387635... and s = 0.5741930515285908458... are roots of the system of equations s*cos(1-exp(s)) = r, 1 + exp(s)*s*tan(1-exp(s)) = 0. - Vaclav Kotesovec, Jul 16 2014

Maple

A:= proc(n) option remember; if n=0 then 0 else convert (series (x* (sec (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

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

Crossrefs

Sequence in context: A194506 A280458 A294198 * A010571 A280248 A067124

Adjacent sequences: A133550 A133551 A133552 * A133554 A133555 A133556

Keyword

nonn

Author

Alois P. Heinz, Aug 27 2008

Status

approved