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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
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
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