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A189054
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E.g.f. exp(x/sqrt(1-4*x^2)).
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1
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1, 1, 1, 13, 49, 841, 6001, 126421, 1371553, 34081489, 503678881, 14391006301, 271223253841, 8751666000793, 201326507146129, 7238365225056421, 197024810845531201, 7810072695945382561, 245787442777437613633
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OFFSET
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0,4
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LINKS
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FORMULA
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a(n) = n! * sum(k=0..n, (binomial((n-2)/2, (n-k)/2) * 2^(n-k-1) * ((-1)^(n-k)+1))/k!).
a(n) ~ (2*n)^(n-1/3) / (sqrt(3)*exp(n-3/4*(2*n)^(1/3))). - Vaclav Kotesovec, Jun 02 2013
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MATHEMATICA
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CoefficientList[Series[Exp[x/Sqrt[1-4*x^2]], {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jun 02 2013 *)
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PROG
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(Maxima)
a(n):= n!*sum((binomial((n-2)/2, (n-k)/2)*2^(n-k-1)*((-1)^(n-k)+1))/k!, k, 0, n);
(PARI) x='x+O('x^66); /* that many terms */
egf=exp(x/sqrt(1-4*x^2)) /* = 1 +x +1/2*x^2 +13/6*x^3 +49/24*x^4 +... */
Vec(serlaplace(egf)) /* show terms */ /* Joerg Arndt, Apr 22 2011 */
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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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