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A102063 Expansion of e.g.f. tan(arctanh(x)), odd powers only. 1
1, 4, 80, 3680, 300800, 38233600, 6960179200, 1715803648000, 549927772160000, 222172054667264000, 110418310176112640000, 66193620737183580160000, 47093975714823012352000000, 39225810499489538768896000000, 37809201187185822383734784000000, 41754105224509634604034949120000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

With alternating signs, expansion of tanh(arctan(x)).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..100

EXAMPLE

tan(arctanh(x)) = x + 4*x^3/3! + 80*x^5/5! + 3680*x^7/7! + 300800*x^9/9! + ...

MAPLE

seq(coeff(series(factorial(n)*tan(arctanh(x)), x, n+1), x, n), n = 1 .. 32, 2); # Muniru A Asiru, Aug 16 2018

MATHEMATICA

nmax=20; Table[(CoefficientList[Series[Tan[ArcTanh[x]], {x, 0, 2*nmax}], x] Range[0, 2 nmax - 1]!)[[n]], {n, 2, 2 nmax, 2}] (* Vincenzo Librandi, Aug 16 2018 *)

PROG

(MAGMA) m:=35; R<x>:=PowerSeriesRing(Rationals(), m);  b:=Coefficients(R!(1+Tan(Argtanh(x)))); [Factorial(n-1)*b[n]: n in [2..m by 2]]; // Vincenzo Librandi, Aug 16 2018

CROSSREFS

Sequence in context: A012824 A012057 A214298 * A002436 A013031 A012923

Adjacent sequences:  A102060 A102061 A102062 * A102064 A102065 A102066

KEYWORD

nonn

AUTHOR

Ralf Stephan, Dec 28 2004

EXTENSIONS

Example corrected by Vaclav Kotesovec, Aug 16 2018

STATUS

approved

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Last modified August 8 12:30 EDT 2022. Contains 356009 sequences. (Running on oeis4.)