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A152029 a(n) = 2^n*(2*n)!/((n+1)!). 3
1, 2, 16, 240, 5376, 161280, 6082560, 276756480, 14760345600, 903333150720, 62412108595200, 4805732361830400, 408117579035443200, 37896632339005440000, 3819980539771748352000, 415422883700177633280000, 48482294191832495554560000, 6044126009248451112468480000 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
K. Casteels and B. Stevens, Universal cycles of (n-1)-partitions of an n-set, Discr. Math., 309 (2009), 5332-5340.
FORMULA
E.g.f 2/(1+(1-8*x)^(1/2)). - Sergei N. Gladkovskii, Oct 26 2012
a(n) = 2^n * A001761(n) = A065140(n)/(n+1)!. - Michel Marcus, Jun 02 2013
G.f.: G(0)/2, where G(k)= 1 + 1/(1 - 2*x/(2*x + (k+2)/((2*k+1)*(2*k+2))/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 03 2013
4*(n+1)*(2*n+1)*a(n) = (n+2)*a(n+1). - Robert Israel, Jan 25 2017
E.g.f.: 1/(1 - 2*x/(1 - 2*x/(1 - 2*x/(1 - 2*x/(1 - 2*x/(1 - ...)))))), a continued fraction. - Ilya Gutkovskiy, May 10 2017
MAPLE
seq(2^n*(2*n)!/(n+1)!, n=0..40); # Robert Israel, Jan 25 2017
MATHEMATICA
Table[(2^n) (2 n)! / (n + 1)!, {n, 0, 20}] (* Vincenzo Librandi, Jan 27 2017 *)
With[{nn=20}, CoefficientList[Series[2/(1+(1-8x)^(1/2)), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Mar 11 2023 *)
PROG
(PARI) a(n) = 2^n*(2*n)!/(n+1)! \\ Michel Marcus, Jun 02 2013
(Magma) [2^n*Factorial(2*n)/Factorial(n+1): n in [0..20]]; // Vincenzo Librandi, Jan 27 2017
CROSSREFS
Sequence in context: A301581 A280394 A223614 * A152069 A188767 A206884
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Sep 15 2009
STATUS
approved

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)