A133596 E.g.f. satisfies: A(x) = x*(sinh(sinh(A(x)))+1).

0, 1, 2, 6, 32, 280, 3192, 43344, 690496, 12726144, 266222880, 6222163200, 160658284800, 4542751030272, 139616399952512, 4634016219678720, 165191949394008064, 6294553527003086848, 255316547059075256832

Offset

0,3

Links

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

Formula

a(n) ~ n^(n-1) * sqrt(s/((s-r)*(cosh(s))^2 + tanh(s))) / (exp(n) * r^n), where r = 0.4068975138196165625... and s = 0.9455473915228318233... are roots of the system of equations r*cosh(s)*cosh(sinh(s)) = 1, s = r + r*sinh(sinh(s)). - Vaclav Kotesovec, Jul 16 2014

Maple

A:= proc(n) option remember; if n=0 then 0 else convert (series (x* (sinh (sinh(A(n-1)))+1), x=0, n+1), polynom) fi end: a:= n-> coeff (A(n), x, n)*n!: seq (a(n), n=0..23);

Mathematica

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

Crossrefs

Sequence in context: A121676 A326096 A346270 * A088437 A191691 A191712

Adjacent sequences: A133593 A133594 A133595 * A133597 A133598 A133599

Keyword

nonn

Author

Alois P. Heinz, Aug 27 2008

Status

approved