A012304 Expansion of e.g.f.: exp(arcsin(x)*log(x+1)).

1, 0, 2, -3, 24, -100, 808, -5439, 51800, -469008, 5292162, -59508075, 782885532, -10464052248, 157781733198, -2437533390915, 41504137389648, -726658147836384, 13799849799221682, -269818493378847219

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..448

Example

E.g.f. = 1 + 2*x^2/2! - 3*x^3/3! + 24*x^4/4! - 100*x^5/5! + ...

Maple

seq(coeff(series(factorial(n)*exp(arcsin(x)*log(x+1)), x, n+1), x, n), n = 0 .. 20); # Muniru A Asiru, Oct 26 2018

Mathematica

With[{nn=20}, CoefficientList[Series[Exp[ArcSin[x]Log[x+1]], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, May 27 2017 *)

Prog

(PARI) x='x+O('x^30); Vec(serlaplace(exp(asin(x)*log(x+1)))) \\ G. C. Greubel, Oct 25 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(Arcsin(x)*Log(x+1)) )); [Factorial(n-1)*b[n]: n in [1..m-1]]; // G. C. Greubel, Oct 25 2018

Crossrefs

Sequence in context: A157327 A174073 A009231 * A047157 A353165 A003221

Adjacent sequences: A012301 A012302 A012303 * A012305 A012306 A012307

Keyword

sign

Author

Patrick Demichel (patrick.demichel(AT)hp.com)

Extensions

Definition clarified by Harvey P. Dale, May 27 2017

Status

approved