A012305 Expansion of e.g.f. arcsin(arcsin(x)*log(x+1)).

0, 0, 2, -3, 12, -40, 358, -2499, 25032, -229104, 2865402, -36173115, 550240020, -8500522680, 149846317710, -2762418635235, 56365118364240, -1205267403147360, 27829436319559410, -674568212738977395

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)*arcsin(arcsin(x)*log(x+1)), x, n+1), x, n), n = 0 .. 20); # Muniru A Asiru, Oct 25 2018

Mathematica

With[{nn=20}, Drop[CoefficientList[Series[ArcSin[ArcSin[x]Log[x+1]], {x, 0, nn}], x] Range[0, nn]!, 2]] (* Harvey P. Dale, Oct 18 2013 *)

Prog

(PARI) x='x+O('x^30); concat([0, 0], Vec(serlaplace(asin(asin(x)* log(x+1))))) \\ G. C. Greubel, Oct 25 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Arcsin(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: A012514 A012511 A012309 * A012512 A012516 A012306

Adjacent sequences: A012302 A012303 A012304 * A012306 A012307 A012308

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