A133892 E.g.f. satisfies: A(x) = x*(tan(sinh(A(x)))+1).

0, 1, 2, 6, 36, 360, 4542, 68544, 1226792, 25441920, 598142170, 15713984000, 456391238028, 14521095333888, 502259604707798, 18763725111828480, 752970270575818192, 32301914469949407232, 1475208429063535282482, 71458043399471257288704, 3659301012147404374818420

Offset

0,3

Links

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

Formula

a(n) ~ n^(n-1) * sqrt(s/((2*r^2-2*r*s+s^2)*(2*(s-r)*(cosh(s))^2 + r*sinh(s)))) / (exp(n) * r^(n-1)), where r = 0.3611557635751972926... and s = 0.7471844338670576493... are roots of the system of equations r*cosh(s) = (cos(sinh(s)))^2, s = r + r*tan(sinh(s)). - Vaclav Kotesovec, Jul 16 2014

Maple

A:= proc(n) option remember; if n=0 then 0 else convert (series (x* (tan (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..25);
# second Maple program:
a:= n-> n!*coeff(series(RootOf(A=x*(tan(sinh(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 + Tan[Sinh[x]]), {x, 0, 20}], x], x] * Range[0, 20]! (* Vaclav Kotesovec, Jul 16 2014 *)

Crossrefs

Cf. A133822.

Sequence in context: A275551 A321085 A133822 * A196870 A089709 A262234

Adjacent sequences: A133889 A133890 A133891 * A133893 A133894 A133895

Keyword

nonn

Author

Alois P. Heinz, Aug 27 2008

Status

approved