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A180680
Expansion of e.g.f. (1 - sqrt(1 - 4*LambertW(x)))/2.
3
1, 0, 9, 8, 705, 2304, 154945, 1097088, 67699233, 821657600, 49591224441, 901894072320, 54967757171041, 1372143152529408, 86054992196720625, 2772416395058315264, 181071792859314812865, 7195828128158173888512, 493215560390253143533033
OFFSET
1,3
LINKS
FORMULA
a(n) = n!*Sum_{k=1..n} (-1)^(n-k)*n^(n-k-1)*binomial(2*(k-1),k-1)/(n-k)!.
a(n) ~ (4/exp(5/4))^n / sqrt(10) * n^(n-1). - Vaclav Kotesovec, Nov 27 2012
E.g.f.: LambertW(x)/(1 - LambertW(x)/(1 - LambertW(x)/(1 - LambertW(x)/(1 - ...)))), a continued fraction. - Ilya Gutkovskiy, Nov 19 2017
MATHEMATICA
Rest[CoefficientList[Series[(1-Sqrt[1-4*LambertW[x]])/2, {x, 0, 20}], x]* Range[0, 20]!] (* Vaclav Kotesovec, Nov 27 2012 *)
PROG
(PARI) x='x+O('x^50); Vec(serlaplace((1 - sqrt(1 - 4*lambertw(x)))/2)) \\ G. C. Greubel, Nov 08 2017
(PARI) a(n) = n!*sum(k=1, n, (-1)^(n-k)*n^(n-k-1)*binomial(2*(k-1), k-1)/(n-k)!); \\ Michel Marcus, Nov 09 2017
CROSSREFS
Sequence in context: A038298 A370935 A013439 * A165398 A329716 A021105
KEYWORD
nonn
AUTHOR
Svetlana Khomich (hsl(AT)cyberline.ru), Sep 15 2010
STATUS
approved