A009805 Expansion of e.g.f. tanh(sinh(x)*sin(x))/2 in odd powers of x^2.

1, -124, 262096, -2681078464, 83993259325696, -6291889632188161024, 963296773204704677810176, -270352239123704851078462357504, 128399592149905444543967414059073536, -97061880731293117665388947647693059784704, 111259126741155511631646423576320132328299954176

Offset: 0

Author

R. H. Hardin

Keywords

• sign

Examples

			x^2/2! - 124*x^6/6! + 262096*x^10/10! - 2681078464*x^14/14! ...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..100

Crossrefs

Cf. A023702.

Programs

Mathematica

Tanh[ Sinh[ x ]*Sin[ x ] ]/2 (* [ x^(4n+2) ] *)
With[{nn=34},Take[CoefficientList[Series[Tanh[Sinh[x]Sin[x]]/2,{x,0,nn}],x] Range[0,nn]!,{3,-1,4}]] (* Harvey P. Dale, May 28 2019 *)

PARI

seq(n)={my(A=O(x^(4*n+2))); Vec(substpol(serlaplace( tanh(sinh(x + A)*sin(x + A))/2 )/x^2, x^4, x))} \\ Andrew Howroyd, Jan 12 2025

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

a(9) onwards from Andrew Howroyd, Jan 12 2025