A012028 E.g.f. sec(sin(arctan(x))) = 1/cos(x/sqrt(1+x^2)).

1, 1, -7, 121, -3823, 186961, -12464695, 967217161, -51115216735, -15922673810399, 12685061907297305, -7463929930799687399, 4531120544938557395633, -3032728078954072676445839

Offset

0,3

Links

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

Formula

E.g.f.: 1/cos(x/sqrt(1+x^2)) = 1 + x^2/(G(0)) where G(k)= 2*(2*k+1)*(k+1)*(1+x^2) - x^2 + 2*(2*k+1)*(k+1)*x^2*(1+x^2)/G(k+1); (continued fraction, Euler's 1st kind, 1-step). - Sergei N. Gladkovskii, Aug 06 2012

Example

sec(sin(arctan(x)))=1+1/2!*x^2-7/4!*x^4+121/6!*x^6-3823/8!*x^8...

Crossrefs

Sequence in context: A095752 A113267 A274267 * A279235 A094088 A012043

Adjacent sequences: A012025 A012026 A012027 * A012029 A012030 A012031

Keyword

sign

Author

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

Status

approved