A012262 Expansion of e.g.f. exp(arctanh(arcsinh(x))).

1, 1, 1, 2, 5, 24, 109, 552, 3177, 28032, 227961, 1778688, 15773229, 212383872, 2521786149, 25215328512, 294715261521, 5734229114880, 91106569198449, 1029078328135680, 14283819393505749, 410202091438571520

Offset

0,4

Comments

a(32) is negative. - Vaclav Kotesovec, Oct 25 2013

Links

Alois P. Heinz, Table of n, a(n) for n = 0..200

Formula

a(n) ~ 8*n^(n-1)*(2*sin(Pi*n/2)-Pi*cos(Pi*n/2))/((4+Pi^2)^(3/2)*exp(n)). - Vaclav Kotesovec, Oct 25 2013

Example

E.g.f. = 1 + x + x^2/2! + 2*x^3/3! + 5*x^4/4! + 24*x^5/5! + ...

Maple

seq(coeff(series(factorial(n)*exp(arctanh(arcsinh(x))), x, n+1), x, n), n = 0 .. 25); # Muniru A Asiru, Oct 29 2018

Mathematica

CoefficientList[Series[Exp[ArcTanh[ArcSinh[x]]], {x, 0, 35}], x]* Range[0, 35]! (* Vaclav Kotesovec, Oct 25 2013 *)

Prog

(PARI) x='x+O('x^30); Vec(serlaplace(exp(atanh(asinh(x))))) \\ G. C. Greubel, Oct 28 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(Argtanh(Argsinh(x))) )); [Factorial(n-1)*b[n]: n in [1..m-1]]; // G. C. Greubel, Oct 28 2018

Crossrefs

Sequence in context: A200402 A010365 A218939 * A012254 A322897 A284230

Adjacent sequences: A012259 A012260 A012261 * A012263 A012264 A012265

Keyword

sign

Author

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

Status

approved