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A012022 E.g.f.: arctan(sin(arctan(x))) (odd powers only). 0
1, -5, 129, -7965, 903105, -163451925, 43259364225, -15764670046125, 7571150452490625, -4634731528895593125, 3522824632122301130625, -3255279003622294051528125, 3593928024032353882700450625 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..12.

FORMULA

a(n) = ((2*n+1)!*(-1)^n*sum(j=1..n+1, binomial((2*n-1)/2,n+1-j) /(2*j-1))).  [From Vladimir Kruchinin, May 19 2011]

E.g.f.: sum(a(n) x^(2n+1)/(2n+1)! = arctan(sin(arctan(x))).

a(n) = (2*n+1)! * [x^(2*n+1)] arctan(sin(arctan(x))).

EXAMPLE

atan(sin(atan(x))) = x - 5/6*x^3 + 43/40*x^5 -+...

MATHEMATICA

With[{nn=30}, Take[CoefficientList[Series[ArcTan[Sin[ArcTan[x]]], {x, 0, nn}], x] Range[0, nn-1]!, {2, -1, 2}]] (* Harvey P. Dale, Dec 11 2013 *)

PROG

(Maxima)

a(n):= ((2*n+1)!* (-1)^n *sum(binomial((2*n-1)/2, n+1-j)/(2*j-1), j, 1, n+1)); [From Vladimir Kruchinin, May 19 2011]

CROSSREFS

Sequence in context: A094074 A012218 A012136 * A012176 A012187 A012083

Adjacent sequences:  A012019 A012020 A012021 * A012023 A012024 A012025

KEYWORD

sign

AUTHOR

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

STATUS

approved

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Last modified November 18 10:38 EST 2017. Contains 294887 sequences.