A013301 - OEIS

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A013301

E.g.f.: arctanh(arctanh(x)-log(x+1)).

0, 1, 6, 150, 7560, 650160, 84823200, 15617281680, 3855823171200, 1229340262550400, 491641405006752000, 241000527467642342400, 142107676844443620710400, 99236357585615999548800000

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

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

FORMULA

a(n) ~ (2*n-1)! / (1-exp(-2))^n. - Vaclav Kotesovec, Feb 05 2015

EXAMPLE

1/2!*x^2 + 6/4!*x^4 + 150/6!*x^6 + 7560/8!*x^8 + ...

MATHEMATICA

nn = 20; Table[(CoefficientList[Series[ArcTanh[ArcTanh[x] - Log[1 + x]], {x, 0, 2*nn}], x] * Range[0, 2*nn]!)[[n]], {n, 1, 2*nn+1, 2}] (* Vaclav Kotesovec, Feb 05 2015 *)

CROSSREFS

Cf. A219863.

Sequence in context: A222051 A285747 A013296 * A233734 A227044 A188420

Adjacent sequences: A013298 A013299 A013300 * A013302 A013303 A013304

KEYWORD

nonn

AUTHOR

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

EXTENSIONS

Definition clarified by Vaclav Kotesovec, Feb 05 2015

Prepended missing a(0)=0 from Vaclav Kotesovec, Feb 05 2015

STATUS

approved