A012608 Expansion of e.g.f. sec(arcsinh(x)*arcsin(x)), powers of x^4 only.

1, 12, 13328, 117619392, 4062867095808, 388601301012237312, 83771183547685073326080, 35504181228757953494366208000, 26841389346007019483917993990225920, 33654478025536204699103406849552997416960, 66134661422427811384963352725241987600886005760

Offset

0,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..110

Formula

a(n) ~ c * 2^(8*n) * n^(4*n-1) / exp(4*n), where c = log(1 + sqrt(2)) * sin(Pi*log(1 + sqrt(2))/2) / cos(Pi*log(1 + sqrt(2))/2)^2 = 25.235157572215940173261389272747... - Vaclav Kotesovec, Aug 25 2025

Example

1 + 12/4!*x^4 + 13328/8!*x^8 + 117619392/12!*x^12...

Mathematica

With[{nn=40}, Take[CoefficientList[Series[Sec[ArcSinh[x]ArcSin[x]], {x, 0, nn}], x]Range[0, nn]!, {1, -1, 4}]] (* Harvey P. Dale, Apr 09 2012 *)

Crossrefs

Sequence in context: A381090 A159413 A317958 * A012735 A012674 A301533

Adjacent sequences: A012605 A012606 A012607 * A012609 A012610 A012611

Keyword

nonn

Author

Patrick Demichel

Extensions

More terms from Harvey P. Dale, Apr 09 2012

Name edited by Jason Yuen, Aug 25 2025

Status

approved