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URL: https://oeis.org/A189054

⇱ A189054 - OEIS

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A189054
Expansion of e.g.f. exp(x/sqrt(1-4*x^2)).
2
1, 1, 1, 13, 49, 841, 6001, 126421, 1371553, 34081489, 503678881, 14391006301, 271223253841, 8751666000793, 201326507146129, 7238365225056421, 197024810845531201, 7810072695945382561, 245787442777437613633, 10650850672760636362669, 380690212524743467643761
OFFSET
0,4
LINKS
FORMULA
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
MATHEMATICA
CoefficientList[Series[Exp[x/Sqrt[1-4*x^2]], {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jun 02 2013 *)
PROG
(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) my(x='x+O('x^30), egf=exp(x/sqrt(1-4*x^2))); Vec(serlaplace(egf)) /* Joerg Arndt, Apr 22 2011 */
CROSSREFS
Cf. A012150.
Sequence in context: A197663 A274784 A294520 * A231947 A322615 A209995
KEYWORD
nonn
AUTHOR
Vladimir Kruchinin, Apr 16 2011
STATUS
approved