login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A012345 Coefficients in the expansion sinh(arcsin(x)*arcsin(x)) = 2*x^2/2!+8*x^4/4!+248*x^6/6!+11328*x^8/8!+... 1
2, 8, 248, 11328, 849312, 94857600, 14819214720, 3091936512000, 831657655349760, 280473756197529600, 115967597965430077440, 57712257892456911912960, 34039765801079493369569280 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..223

FORMULA

a(n) ~ sqrt(Pi) * cosh(Pi^2/4) * (2*n)! / (2 * n^(3/2)). - Vaclav Kotesovec, Feb 08 2015

EXAMPLE

sinh(arcsin(x)*arcsin(x)) = 2*x^2/2! + 8*x^4/4! + 248*x^6/6! + 11328*x^8/8! + ...

MATHEMATICA

nn = 20; Table[(CoefficientList[Series[Sinh[ArcSin[x]^2], {x, 0, 2*nn}], x] * Range[0, 2*nn]!)[[n]], {n, 1, 2*nn+1, 2}] (* Vaclav Kotesovec, Feb 08 2015 *)

PROG

(PARI) x='x+O('x^50); v=Vec(serlaplace(sinh(asin(x)*asin(x)))); vector(#v\2, n, v[2*n-1]) \\ G. C. Greubel, Apr 11 2017

CROSSREFS

Sequence in context: A028985 A067583 A120378 * A012341 A299374 A203317

Adjacent sequences: A012342 A012343 A012344 * A012346 A012347 A012348

KEYWORD

nonn

AUTHOR

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

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 7 19:19 EST 2022. Contains 358669 sequences. (Running on oeis4.)