A012267 Expansion of e.g.f. arcsin(log(x+1)^2).

0, 0, 2, -6, 22, -100, 668, -6048, 64776, -763488, 9918072, -144472680, 2365739880, -42879666960, 845124232080, -17930092309920, 408038138491200, -9939819541747200, 258294825756089760, -7127596576224545760

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..418 (terms 0..60 from Muniru A Asiru)

Formula

a(n) ~ (-1)^n * sqrt(2) * n^(n-1) / (exp(1) - 1)^(n - 1/2). - Vaclav Kotesovec, Jul 17 2018

Example

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

Maple

seq(coeff(series(factorial(n)*arcsin(log(x+1)^2), x, n+1), x, n), n=0..20); # Muniru A Asiru, Jul 17 2018

Mathematica

With[{nn = 30}, CoefficientList[Series[ArcSin[Log[x + 1]^2], {x, 0, nn}], x] Range[0, nn]!] (* G. C. Greubel, Oct 28 2018 *)

Prog

(PARI) x = 'x + O('x^30); concat([0, 0], Vec(serlaplace(asin(log(x+1)^2)))) \\ Michel Marcus, Jul 17 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Arcsin(Log(x+1)^2) )); [0, 0] cat [Factorial(n+1)*b[n]: n in [1..m-2]]; // G. C. Greubel, Oct 25 2018

Crossrefs

Sequence in context: A245119 A012270 A009585 * A012268 A009655 A002772

Adjacent sequences: A012264 A012265 A012266 * A012268 A012269 A012270

Keyword

sign

Author

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

Extensions

a(0) and a(1) inserted by Sean A. Irvine, Jul 16 2018

Name clarified by Michel Marcus, Jul 17 2018

Status

approved