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A205571
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E.g.f.: 1/(1 - x*cosh(x)).
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8
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1, 1, 2, 9, 48, 305, 2400, 22057, 230272, 2708001, 35412480, 509177801, 7986468864, 135718942801, 2483729876992, 48699677975145, 1018542257111040, 22634000289407297, 532557637644976128, 13226748101381102473, 345792863300174479360, 9492229607399841038961
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OFFSET
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0,3
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COMMENTS
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Radius of convergence of e.g.f. is |x| < r where r = 0.7650099545507... satisfies cosh(r) = 1/r. See A069814.
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LINKS
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FORMULA
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a(2*n-1) == 1 (mod 4), a(2*n+2) == 0 (mod 4), for n>=1.
a(n) ~ n!/(1+r*sqrt(1-r^2))*(1/r)^n, where r = 0.7650099545507321... is the root of the equation r*cosh(r)=1. - Vaclav Kotesovec, Feb 13 2013
a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} binomial(n,2*k+1) * (2*k+1) * a(n-2*k-1). - Ilya Gutkovskiy, Mar 10 2022
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EXAMPLE
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E.g.f.: A(x) = 1 + x + 2*x^2/2! + 9*x^3/3! + 48*x^4/4! + 305*x^5/5! +...
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MATHEMATICA
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CoefficientList[Series[1/(1-x*Cosh[x]), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Feb 13 2013 *)
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PROG
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(PARI) {a(n)=n!*polcoeff(1/(1-x*cosh(x +x*O(x^n))), n)}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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