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

Extensions

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

Name clarified by Michel Marcus, Jul 17 2018

Status

approved