A133984 E.g.f. satisfies: A(x) = x*(tan(exp(A(x))-1)+1).

0, 1, 2, 9, 72, 845, 12972, 244741, 5468176, 141111693, 4129615540, 135127313101, 4888457921688, 193733261456605, 8346805786382364, 388432439875807125, 19417284993350451232, 1037672210204182995277, 59035412382992193993732

Offset

0,3

Links

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

Formula

a(n) ~ n^(n-1) * sqrt(r*s/(r+2*exp(s)*(s-r))) / (exp(n) * r^n), where r = 0.2898872767597687473... and s = 0.5719846912143595905... are roots of the system of equations s+r*tan(1-exp(s)) = r, exp(s)*r = (cos(1-exp(s)))^2. - Vaclav Kotesovec, Jul 16 2014

Maple

A:= proc(n) option remember; if n=0 then 0 else convert (series (x* (tan (exp(A(n-1))-1)+1), x=0, n+1), polynom) fi end: a:= n-> coeff (A(n), x, n)*n!: seq (a(n), n=0..22);

Mathematica

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

Crossrefs

Sequence in context: A133941 A240956 A038035 * A208898 A108995 A184358

Adjacent sequences: A133981 A133982 A133983 * A133985 A133986 A133987

Keyword

nonn

Author

Alois P. Heinz, Aug 27 2008

Status

approved