A102063 Expansion of e.g.f. tan(arctanh(x)), odd powers only.

1, 4, 80, 3680, 300800, 38233600, 6960179200, 1715803648000, 549927772160000, 222172054667264000, 110418310176112640000, 66193620737183580160000, 47093975714823012352000000, 39225810499489538768896000000, 37809201187185822383734784000000, 41754105224509634604034949120000000

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