

A009105


Expansion of e.g.f. cos(x)/cos(sinh(x)), even powers only.


1



1, 0, 4, 56, 2192, 128448, 11141824, 1332816512, 210250492160, 42290401757184, 10563624419906560, 3208072210301966336, 1164053448822395604992, 497366043438147538010112, 247165485059674632625438720
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OFFSET

0,3


LINKS

G. C. Greubel, Table of n, a(n) for n = 0..232


FORMULA

a(n) ~ (2*n)! * 4 * cos(arcsinh(Pi/2)) / (sqrt(4+Pi^2) * arcsinh(Pi/2)^(2*n+1)).  Vaclav Kotesovec, Jan 22 2015


MATHEMATICA

nn = 20; Table[(CoefficientList[Series[Cos[x]*Sec[Sinh[x]], {x, 0, 2*nn}], x] * Range[0, 2*nn]!)[[n]], {n, 1, 2*nn+1, 2}] (* Vaclav Kotesovec, Jan 22 2015 *)


PROG

(PARI) x='x+O('x^50); v=Vec(serlaplace(cos(x)/cos(sinh(x)))); vector(#v\2, n, v[2*n1]) \\ G. C. Greubel, Jul 26 2018


CROSSREFS

Sequence in context: A012983 A012959 A013113 * A168481 A171801 A091797
Adjacent sequences: A009102 A009103 A009104 * A009106 A009107 A009108


KEYWORD

nonn


AUTHOR

R. H. Hardin


EXTENSIONS

Extended and signs tested by Olivier Gérard, Mar 15 1997


STATUS

approved



