A012622 Expansion of e.g.f. exp(arcsinh(x)*arctan(x)) (even powers only).

1, 2, 0, -2, 56, -2358, 136092, -8379282, -86371632, 375439810578, -214530925771068, 116413070752178550, -68704024823157716040, 45584029026653621816730, -34279883031448204487212500

Offset

0,2

Links

Robert Israel, Table of n, a(n) for n = 0..225

Example

1 + (2/2!)*x^2 - (2/6!)*x^6 + (56/8!)*x^8 - (2358/10!)*x^10 ...

Maple

S:= series(exp(arcsinh(x)*arctan(x)), x, 51):
seq(coeff(S, x, 2*j)*(2*j)!, j=0..25); # Robert Israel, Apr 12 2019

Mathematica

With[{nn=30}, Take[CoefficientList[Series[Exp[ArcSinh[x]ArcTan[x]], {x, 0, nn}], x] Range[0, nn]!, {1, -1, 2}]] (* Harvey P. Dale, Sep 05 2019 *)

Crossrefs

Sequence in context: A056949 A346235 A281326 * A013370 A013374 A013371

Adjacent sequences: A012619 A012620 A012621 * A012623 A012624 A012625

Keyword

sign

Author

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

Status

approved