A012275 Expansion of e.g.f. arcsin(exp(x)*log(x+1)).

1, 1, 3, 6, 53, 235, 2709, 20188, 278249, 3019693, 48281695, 692436338, 12717929157, 225943945071, 4727712830281, 99660715587704, 2354596166060273, 57197420701626009, 1511830772603161339

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..421

Example

E.g.f. = x + x^2/2! + 3*x^3/3! + 6*x^4/4! + 53*x^5/5! + ...

Maple

seq(coeff(series(factorial(n)*arcsin(exp(x)*log(x+1)), x, n+1), x, n), n = 0 .. 20); # Muniru A Asiru, Oct 28 2018

Mathematica

With[{nn = 30}, CoefficientList[Series[ArcSin[Exp[x]*Log[x+1]], {x, 0, nn}], x] Range[0, nn]!] (* G. C. Greubel, Oct 28 2018 *)

Prog

(PARI) x='x+O('x^30); Vec(serlaplace(asin(exp(x)*log(x+1)))) \\ G. C. Greubel, Oct 28 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Arcsin(Exp(x)*Log(x+1)) )); [Factorial(n)*b[n]: n in [1..m-1]]; // G. C. Greubel, Oct 28 2018

Crossrefs

Sequence in context: A056447 A056437 A309320 * A067608 A023177 A132474

Adjacent sequences: A012272 A012273 A012274 * A012276 A012277 A012278

Keyword

nonn

Author

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

Status

approved