A012571 Expansion of arcsin(sinh(x)*sinh(x)).

0, 2, 8, 152, 6848, 554912, 70690688, 13009484672, 3265063958528, 1071643508306432, 445538702940858368, 228823524775428872192, 142264706412727018078208, 105297877340452669962493952

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..220

Formula

a(n) ~ (2*n)! / (2^(1/4) * sqrt(Pi) * n^(3/2) * (log(1+sqrt(2)))^(2*n-1/2)). - Vaclav Kotesovec, Feb 06 2015

Example

arcsin(sinh(x)*sinh(x)) = 2/2!*x^2+8/4!*x^4+152/6!*x^6+6848/8!*x^8...

Mathematica

With[{nn=30}, Take[CoefficientList[Series[ArcSin[Sinh[x]^2], {x, 0, nn}], x] Range[0, nn]!, {1, -1, 2}]] (* Harvey P. Dale, Dec 11 2013 *)

Crossrefs

Appears to equal 2 * A012101.

Sequence in context: A102099 A012298 A009596 * A018926 A012432 A071097

Adjacent sequences: A012568 A012569 A012570 * A012572 A012573 A012574

Keyword

nonn

Author

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

Extensions

a(0)=0 prepended by Vaclav Kotesovec, Feb 06 2015

Status

approved