A189054 E.g.f. exp(x/sqrt(1-4*x^2)).

1, 1, 1, 13, 49, 841, 6001, 126421, 1371553, 34081489, 503678881, 14391006301, 271223253841, 8751666000793, 201326507146129, 7238365225056421, 197024810845531201, 7810072695945382561, 245787442777437613633

Offset

0,4

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

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) 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 */

Crossrefs

Sequence in context: A197663 A274784 A294520 * A231947 A322615 A209995

Adjacent sequences: A189051 A189052 A189053 * A189055 A189056 A189057

Keyword

nonn

Author

Vladimir Kruchinin, Apr 16 2011

Status

approved