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 A012267 Expansion of e.g.f. arcsin(log(x+1)^2). 1
 0, 0, 2, -6, 22, -100, 668, -6048, 64776, -763488, 9918072, -144472680, 2365739880, -42879666960, 845124232080, -17930092309920, 408038138491200, -9939819541747200, 258294825756089760, -7127596576224545760 (list; graph; refs; listen; history; text; internal format)
 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:=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

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Last modified March 24 19:39 EDT 2019. Contains 321448 sequences. (Running on oeis4.)