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A205570
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E.g.f.: 1/sqrt(1+x^2 - 2*x*cosh(x)).
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2
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1, 1, 2, 9, 60, 485, 4680, 53557, 709968, 10662633, 178786080, 3312164801, 67201649856, 1481949570829, 35291569832064, 902631317654445, 24676916031310080, 718135040275928657, 22164641043514532352, 723163494821506484473, 24869366907327781002240
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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 = LambertW(1) = exp(-LambertW(1)) = 0.56714329040978...
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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! * exp(c*n)/(sqrt(Pi*n)*(1+c)*sqrt(1-c)), where c = LambertW(1) = 0.5671432904... - Vaclav Kotesovec, Jun 26 2013
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EXAMPLE
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E.g.f.: A(x) = 1 + x + 2*x^2/2! + 9*x^3/3! + 60*x^4/4! + 485*x^5/5! +...
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MATHEMATICA
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CoefficientList[Series[1/Sqrt[1+x^2-2*x*Cosh[x]], {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jun 26 2013 *)
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PROG
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(PARI) {a(n)=n!*polcoeff(1/sqrt(1+x^2-2*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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