A133939 E.g.f. satisfies: A(x) = x*(tan(tan(A(x)))+1).

0, 1, 2, 6, 40, 440, 5952, 97104, 1888640, 42480000, 1082119680, 30814080000, 970187827200, 33461288899584, 1254539018571776, 50803163905751040, 2209862882578300928, 102761280728930287616, 5087062588875762696192, 267101579060996713611264

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..200

Formula

a(n) ~ n^(n-1) * (cos(s))^(3/2) * sqrt(s/(-2*r + 2*s + r*sin(2*s))) / (exp(n) * (2*r^2-2*r*s+s^2)^(1/4) * r^(n-3/4)), where r = 0.3331897707672964894... and s = 0.6497639144980735763... are roots of the system of equations r*(sec(s)*sec(tan(s)))^2 = 1, s = r + r*tan(tan(s)). - Vaclav Kotesovec, Jul 16 2014

Maple

A:= proc(n) option remember; if n=0 then 0 else convert(series(x*
       (tan(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..23);

Mathematica

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

Crossrefs

Sequence in context: A292407 A274275 A081471 * A045846 A238818 A199574

Adjacent sequences: A133936 A133937 A133938 * A133940 A133941 A133942

Keyword

nonn

Author

Alois P. Heinz, Aug 27 2008

Status

approved