A013435 E.g.f.: arcsinh(arctanh(x) - arcsin(x)) (odd powers only).

0, 1, 15, 495, 29015, 2666475, 354343275, 64361872575, 15331195839375, 4639834754377875, 1739923436670397875, 792214640482949058375, 430673843640390204684375, 275621285783640234105646875, 205164378528197702536594546875, 175791115887829825909515376359375

Offset

0,3

Links

Robert Israel, Table of n, a(n) for n = 0..224

Example

0*x^1 + (1/3!)*x^3 + (15/5!)*x^5 + (495/7!)*x^7 + (29015/9!*x^9) + ...

Maple

E:= arcsinh(arctanh(x)-arcsin(x)):
S:= series(E, x, 32):
seq(coeff(S, x, k)*k!, k=1..31, 2); # Robert Israel, Aug 07 2018

Mathematica

With[{nn=30}, Join[{0}, Take[CoefficientList[Series[-ArcSinh[ArcSin[x]- ArcTanh[x]], {x, 0, nn}], x]Range[0, nn-1]!, {6, -1, 2}]]] (* Harvey P. Dale, Jul 20 2012 *)
Union[Range[0, 31]! CoefficientList[ Series[ArcSinh[ArcTanh[x] - ArcSin[x]], {x, 0, 31}], x]] (* Robert G. Wilson v, Aug 06 2018 *)

Prog

(PARI)
x='x+O('x^66);
egf=asinh(atanh(x)-asin(x));
v=Vec(serlaplace(egf));
v=vector(#v\2, n, if(n==1, 0, v[2*n-1]))
/* Joerg Arndt, Jul 20 2012 */

Crossrefs

Sequence in context: A377045 A208624 A013433 * A151816 A013431 A013432

Adjacent sequences: A013432 A013433 A013434 * A013436 A013437 A013438

Keyword

nonn

Author

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

Extensions

Definition corrected by Harvey P. Dale, Jul 20 2012

Missing a(1)=1 inserted and offset corrected by Sean A. Irvine, Aug 06 2018

Status

approved