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A012271 Expansion of e.g.f. arcsinh(log(x+1)*log(x+1)). 1
0, 0, 2, -6, 22, -100, 428, -1008, -12504, 325152, -5267448, 72020520, -835748520, 6577169040, 36671947440, -3513587807520, 114499586712000, -2893590831936000, 61563908486205600, -1035793335840588000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..425

FORMULA

Lim sup n->infinity (|a(n)|/n!)^(1/n) = 1.4236247666... = exp(1/sqrt(2))/sqrt(1+exp(sqrt(2)) - 2*exp(1/sqrt(2))*cos(1/sqrt(2))). - Vaclav Kotesovec, Nov 02 2013

EXAMPLE

E.g.f. = 2*x^2/2! - 6*x^3/3! + 22*x^4/4! - 100*x^5/5! + ...

MAPLE

seq(coeff(series(factorial(n)*arcsinh(log(x+1)*log(x+1)), x, n+1), x, n), n = 0 .. 20); # Muniru A Asiru, Oct 28 2018

MATHEMATICA

CoefficientList[Series[ArcSinh[Log[x+1]*Log[x+1]], {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 30 2013 *)

PROG

(PARI) x='x+O('x^30); concat([0, 0], Vec(serlaplace(asinh(log(x+1)^2)))) \\ G. C. Greubel, Oct 28 2018

(MAGMA) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Argsinh(Log(x+1)^2) )); [0, 0] cat [Factorial(n+1)*b[n]: n in [1..m-2]]; // G. C. Greubel, Oct 28 2018

CROSSREFS

Sequence in context: A012269 A012272 A009789 * A012266 A009468 A088819

Adjacent sequences:  A012268 A012269 A012270 * A012272 A012273 A012274

KEYWORD

sign

AUTHOR

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

EXTENSIONS

Prepended missing a(0)=0, a(1)=0 from Vaclav Kotesovec, Nov 02 2013

STATUS

approved

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Last modified April 21 17:36 EDT 2021. Contains 343156 sequences. (Running on oeis4.)