

A012251


exp(arcsinh(arctan(x)))=1+x+1/2!*x^22/3!*x^311/4!*x^4+24/5!*x^5...


2



1, 1, 1, 2, 11, 24, 349, 720, 22455, 40320, 2465241, 3628800, 416217603, 479001600, 100729124469, 87178291200, 33198564667887, 20922789888000, 14328891118054449, 6402373705728000, 7852649782447649403
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,4


LINKS

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


FORMULA

E.g.f.: Q(0)1, where Q(k) = 2 + arctan(x)/(1  arctan(x)/Q(k+1) ); (continued fraction).  Sergei N. Gladkovskii, Dec 19 2013


MATHEMATICA

With[{nn=30}, CoefficientList[Series[Exp[ArcSinh[ArcTan[x]]], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Oct 26 2011 *)


CROSSREFS

Bisections are (1)^n*A010050 and (1)^n*A012138.
Sequence in context: A220281 A009189 A012213 * A241238 A077482 A141428
Adjacent sequences: A012248 A012249 A012250 * A012252 A012253 A012254


KEYWORD

sign


AUTHOR

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


STATUS

approved



