A012089 tan(arcsin(arctan(x)))=x+1/3!*x^3+9/5!*x^5+57/7!*x^7+5169/9!*x^9...

1, 1, 9, 57, 5169, -93807, 31981689, -3857766903, 1058896281825, -286891166986335, 108826313005021545, -47766338018402914215, 25721485923005221938705, -16179153687877979599066575

Offset

0,3

Links

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

Formula

a(n)=(2*n+1)!*sum(m=0..n, binomial(2*m,m)*2^(-4*m-1)*(2*m+1)!*(-1)^(n+m)*sum(i=2*m+1..2*n+1, (2^i*stirling1(i,2*m+1)*binomial(2*n,i-1))/i!)). [Vladimir Kruchinin, Jun 15 2011]

Mathematica

With[{nn=30}, Take[CoefficientList[Series[Tan[ArcSin[ArcTan[x]]], {x, 0, nn}], x] Range[0, nn-1]!, {2, -1, 2}]] (* Harvey P. Dale, Jun 12 2017 *)

Prog

(Maxima)
a(n):=(2*n+1)!*sum(binomial(2*m, m)*2^(-4*m-1)*(2*m+1)!*(-1)^(n+m)*sum((2^i*stirling1(i, 2*m+1)*binomial(2*n, i-1))/i!, i, 2*m+1, 2*n+1), m, 0, n); [Vladimir Kruchinin, Jun 15 2011]

Crossrefs

Sequence in context: A009060 A112616 A197673 * A343133 A044147 A044528

Adjacent sequences: A012086 A012087 A012088 * A012090 A012091 A012092

Keyword

sign

Author

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

Status

approved