A133822 E.g.f. satisfies: A(x) = x*(sinh(tan(A(x)))+1).

0, 1, 2, 6, 36, 360, 4542, 68544, 1226344, 25409664, 596628250, 15651680000, 453879958092, 14417575231488, 497825878940054, 18565202648401920, 743653004987969360, 31843195958676979712, 1451524546915205994162, 70176819912743307902976, 3586765354156262980637940

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..150

Formula

a(n) ~ n^(n-1) * cos(s) * sqrt(s/((s-r)/(cos(s))^2 + sin(2*s))) / (exp(n) * r^n), where r = 0.3619195105630926952... and s = 0.7527256881820097467... are roots of the system of equations r*cosh(tan(s)) = (cos(s))^2, s = r + r*sinh(tan(s)). - Vaclav Kotesovec, Jul 16 2014

Maple

A:= proc(n) option remember; if n=0 then 0 else convert (series (x* (sinh (tan(A(n-1)))+1), x=0, n+1), polynom) fi end: a:= n-> coeff (A(n), x, n)*n!: seq (a(n), n=0..25);
# second Maple program:
a:= n-> n!*coeff(series(RootOf(A=x*(sinh(tan(A))+1), A), x, n+1), x, n):
seq(a(n), n=0..25);  # Alois P. Heinz, Mar 05 2013

Mathematica

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

Crossrefs

Cf. A133892.

Sequence in context: A055541 A275551 A321085 * A133892 A196870 A089709

Adjacent sequences: A133819 A133820 A133821 * A133823 A133824 A133825

Keyword

nonn

Author

Alois P. Heinz, Aug 27 2008

Status

approved