A012351 sech(arcsin(x)*arcsin(x))=1-12/4!*x^4-240/6!*x^6-1008/8!*x^8...

1, 0, -12, -240, -1008, 378240, 32163648, -363487488, -690754821888, -145507353366528, -11585562008128512, 3150884675987558400, 573373842109571665920, -1149448245885758287872000

Offset

0,3

Links

Table of n, a(n) for n=0..13.

Formula

a(n) ~ -sqrt(Pi) * sinh(Pi^2/4) * (2*n)! / (n^(3/2) * (1 + cosh(Pi^2/2))). - Vaclav Kotesovec, Feb 08 2015

Mathematica

nn = 20; Table[(CoefficientList[Series[Sech[ArcSin[x]^2], {x, 0, 2*nn}], x] * Range[0, 2*nn]!)[[n]], {n, 1, 2*nn+1, 2}] (* Vaclav Kotesovec, Feb 08 2015 *)

Crossrefs

Sequence in context: A279610 A222702 A352700 * A189883 A033469 A012544

Adjacent sequences: A012348 A012349 A012350 * A012352 A012353 A012354

Keyword

sign

Author

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

Status

approved