A012185 Expansion of e.g.f.: exp(arctan(sin(x)))=1+x+1/2!*x^2-2/3!*x^3-11/4!*x^4+16/5!*x^5...

1, 1, 1, -2, -11, 16, 301, -272, -16631, 256, 1543801, 1758208, -216765251, -549115904, 42924800101, 178127730688, -11404529749871, -68157333438464, 3916428205369201, 31349506823815168, -1688780438764074491

Offset

0,4

Links

Table of n, a(n) for n=0..20.

Formula

E.g.f.: 1 + 2*sin(x)/(Q(0)-sin(x)), where Q(k) = 4*k+2 + (sin(x))^2*(4*k^2+8*k+5)/Q(k+1) ; (continued fraction). - Sergei N. Gladkovskii, Dec 18 2013

Mathematica

With[{nn=20}, CoefficientList[Series[Exp[ArcTan[Sin[x]]], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Jan 28 2015 *)

Crossrefs

Sequence in context: A306278 A199397 A012019 * A012253 A103336 A019402

Adjacent sequences: A012182 A012183 A012184 * A012186 A012187 A012188

Keyword

sign

Author

Patrick Demichel (patrick.demichel(AT)hp.com)

Extensions

Definition clarified by Harvey P. Dale, Jan 28 2015

Status

approved