A012519 Expansion of e.g.f. arcsin(sinh(x) * exp(x)).

0, 1, 2, 5, 20, 125, 1022, 10145, 119240, 1621625, 25018202, 431595485, 8233157660, 172077583925, 3910293621782, 95985774268025, 2531103994315280, 71356674948823025, 2141700448802291762

Offset

0,3

Links

Muniru A Asiru, Table of n, a(n) for n = 0..100

Formula

E.g.f.: arcsin(sinh(x) * exp(x)).

Example

x + 2/2!*x^2 + 5/3!*x^3 + 20/4!*x^4 + 125/5!*x^5 ...

Maple

seq(coeff(series(factorial(n)*arcsin(sinh(x)*exp(x)), x, n+1), x, n), n=0..20); # Muniru A Asiru, Jul 19 2018

Mathematica

With[{nn=20}, CoefficientList[Series[ArcSin[Sinh[x]Exp[x]], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, May 11 2025 *)

Crossrefs

Sequence in context: A112833 A144503 A012321 * A076795 A130293 A156073

Adjacent sequences: A012516 A012517 A012518 * A012520 A012521 A012522

Keyword

nonn

Author

Patrick Demichel

Extensions

a(0) inserted and title improved by Sean A. Irvine, Jul 19 2018

Status

approved