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
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