

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
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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*n1]) \\ 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



