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 A012312 Expansion of e.g.f. arctanh(arcsin(x) * log(x+1)). 1
 0, 0, 2, -3, 12, -40, 478, -3759, 40152, -387864, 5203962, -70961715, 1142838180, -18621542160, 342700299030, -6622936396335, 140637395893680, -3129194141386320, 74723900156463090, -1873298738386231875 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS G. C. Greubel, Table of n, a(n) for n = 0..426 EXAMPLE E.g.f. = 2*x^2/2! - 3*x^3/3! + 12*x^4/4! - 40*x^5/5! + ... MAPLE seq(coeff(series(factorial(n)*arctanh(arcsin(x)*log(x+1)), x, n+1), x, n), n = 0 .. 20); # Muniru A Asiru, Oct 25 2018 MATHEMATICA With[{nn = 30}, CoefficientList[Series[ArcTanh[ArcSin[x] Log[x + 1]], {x, 0, nn}], x] Range[0, nn]!] (* G. C. Greubel, Oct 25 2018 *) PROG (PARI) x='x+O('x^30); concat([0, 0], Vec(serlaplace(atanh(asin(x)* log(x+1)) ))) \\ G. C. Greubel, Oct 25 2018 (Magma) m:=30; R:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Argtanh(Arcsin(x)*Log(x+1)) )); [0, 0] cat [Factorial(n+1)*b[n]: n in [1..m-2]]; // G. C. Greubel, Oct 25 2018 CROSSREFS Sequence in context: A012512 A012516 A012306 * A009243 A232864 A307957 Adjacent sequences: A012309 A012310 A012311 * A012313 A012314 A012315 KEYWORD sign AUTHOR Patrick Demichel (patrick.demichel(AT)hp.com) EXTENSIONS a(0) and a(1) inserted and title improved by Sean A. Irvine, Jul 17 2018 STATUS approved

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Last modified April 1 19:13 EDT 2023. Contains 361695 sequences. (Running on oeis4.)