A012029 E.g.f.: sech(sin(arctan(x))) (even powers only).

1, -1, 17, -721, 56993, -7232161, 1344866225, -344599447921, 116382225519425, -50097660050713921, 26773024797675332945, -17392081348966913859601, 13497082647397365780254177

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..50

Formula

a(n) ~ (-1)^n * 2^(2*n+5) * n^(2*n+1/2) * (Pi^2+4)^(n-1) / (exp(2*n) * Pi^(2*n+1/2)). - Vaclav Kotesovec, Nov 08 2013

Example

sech(sin(arctan(x))) = 1 -1/2!*x^2 +17/4!*x^4 -721/6!*x^6 +56993/8!*x^8 ...

Mathematica

With[{nn=30}, Take[CoefficientList[Series[Sech[Sin[ArcTan[x]]], {x, 0, nn}], x] Range[0, nn]!, {1, -1, 2}]] (* Harvey P. Dale, Oct 03 2013 *)

Crossrefs

Sequence in context: A309410 A201311 A012182 * A012193 A128274 A012085

Adjacent sequences: A012026 A012027 A012028 * A012030 A012031 A012032

Keyword

sign

Author

Patrick Demichel

Status

approved