A012521 E.g.f.: arctanh(sinh(x)*exp(x)).

0, 1, 2, 6, 32, 240, 2192, 23856, 303872, 4427520, 72545792, 1320608256, 26445350912, 577722163200, 13672510932992, 348466876717056, 9515645659185152, 277168473987809280, 8577847096804769792, 281084141232170336256, 9722444816080638574592, 353990026542011001077760

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Formula

E.g.f.: A(x) = arctanh(x) o x/(1-x) o tanh(x), a composition of functions involving tanh(x) and its inverse; thus, the n-th iteration of A(x) equals arctanh(x) o x/(1-n*x) o tanh(x). [From Paul D. Hanna, Nov 29 2011]

a(n) ~ (n-1)! * 2^(n-1) / (log(3))^n. - Vaclav Kotesovec, Oct 24 2013

Example

E.g.f.: x + 2/2!*x^2 + 6/3!*x^3 + 32/4!*x^4 + 240/5!*x^5 +...

Mathematica

With[{nn=20}, CoefficientList[Series[ArcTanh[Sinh[x]Exp[x]], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Oct 14 2012 *)

Prog

(PARI){a(n)=n!*polcoeff(subst(atanh(x+x*O(x^n)), x, subst(x/(1-x), x, tanh(x+x*O(x^n)))), n)} /* Paul D. Hanna */

Crossrefs

Sequence in context: A261398 A009686 A012318 * A211195 A346452 A012324

Adjacent sequences: A012518 A012519 A012520 * A012522 A012523 A012524

Keyword

nonn

Author

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

Extensions

Prepended a(0)=0, Joerg Arndt, Oct 14 2012

Status

approved