A012317 Expansion of e.g.f. arcsin(arcsin(x) * exp(x)).

0, 1, 2, 5, 20, 133, 1070, 10705, 125512, 1717321, 26518138, 459336605, 8787628060, 184388779469, 4205082557286, 103631769297641, 2743399950572304, 77654985344871313, 2340183966373322610

Offset

0,3

Links

Robert Israel, Table of n, a(n) for n = 0..410

Example

E.g.f. = x + 2/2!*x^2 + 5/3!*x^3 + 20/4!*x^4 + 133/5!*x^5 ...

Maple

S:= series(arcsin(arcsin(x)*exp(x)), x, 51):
seq(coeff(S, x, j)*j!, j=0..50); # Robert Israel, Oct 25 2018

Mathematica

With[{nmax = 30}, CoefficientList[Series[ArcSin[ArcSin[x]*Exp[x]], {x, 0, nmax}], x]*Range[0, nmax]!] (* G. C. Greubel, Oct 25 2018 *)

Prog

(PARI) x='x+O('x^30); concat([0], Vec(serlaplace( asin(asin(x)*exp(x))))) \\ G. C. Greubel, Oct 25 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Arcsin(Arcsin(x)*Exp(x)))); [0] cat [Factorial(n)*b[n]: n in [1..m-1]]; // G. C. Greubel, Oct 25 2018

Crossrefs

Sequence in context: A130293 A156073 A006366 * A297630 A297629 A118181

Adjacent sequences: A012314 A012315 A012316 * A012318 A012319 A012320

Keyword

nonn

Author

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

Extensions

a(0) inserted and title improved by Sean A. Irvine, Jul 17 2018

Status

approved