A012634 E.g.f.: exp(arcsinh(x)*cos(x))=1+x+1/2!*x^2-3/3!*x^3-15/4!*x^4-15/5!*x^5...

1, 1, 1, -3, -15, -15, 225, 1029, -3423, -46239, 58305, 2582701, -3367023, -223494895, 750974497, 31551766453, -195722347967, -6578644464703, 56832659001729, 1828823841664733, -19485490128305615

Offset

0,4

Links

Table of n, a(n) for n=0..20.

Formula

E.g.f.: (x+sqrt(1+x^2))^(cos(x)). - Vaclav Kotesovec, Nov 01 2013

a(n) ~ 2*cosh(1) * sin((n-cosh(1))*Pi/2) * n^(n-1) / exp(n). - Vaclav Kotesovec, Nov 01 2013

Mathematica

With[{nn=30}, CoefficientList[Series[Exp[ArcSinh[x]Cos[x]], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Sep 09 2012 *)

Crossrefs

Sequence in context: A120467 A323499 A332961 * A043060 A029476 A154317

Adjacent sequences: A012631 A012632 A012633 * A012635 A012636 A012637

Keyword

sign

Author

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

Extensions

Definition clarified by Harvey P. Dale, Sep 09 2012

Status

approved