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%I #18 Apr 25 2016 11:45:32
%S 1,1,1,13,49,841,6001,126421,1371553,34081489,503678881,14391006301,
%T 271223253841,8751666000793,201326507146129,7238365225056421,
%U 197024810845531201,7810072695945382561,245787442777437613633
%N E.g.f. exp(x/sqrt(1-4*x^2)).
%H Vincenzo Librandi, <a href="/A189054/b189054.txt">Table of n, a(n) for n = 0..200</a>
%F a(n) = n! * sum(k=0..n, (binomial((n-2)/2, (n-k)/2) * 2^(n-k-1) * ((-1)^(n-k)+1))/k!).
%F a(n) ~ (2*n)^(n-1/3) / (sqrt(3)*exp(n-3/4*(2*n)^(1/3))). - _Vaclav Kotesovec_, Jun 02 2013
%t CoefficientList[Series[Exp[x/Sqrt[1-4*x^2]], {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Jun 02 2013 *)
%o (Maxima)
%o a(n):= n!*sum((binomial((n-2)/2,(n-k)/2)*2^(n-k-1)*((-1)^(n-k)+1))/k!, k,0,n);
%o (PARI) x='x+O('x^66); /* that many terms */
%o egf=exp(x/sqrt(1-4*x^2)) /* = 1 +x +1/2*x^2 +13/6*x^3 +49/24*x^4 +... */
%o Vec(serlaplace(egf)) /* show terms */ /* Joerg Arndt, Apr 22 2011 */
%K nonn
%O 0,4
%A _Vladimir Kruchinin_, Apr 16 2011
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