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A097801 a(n) = (2*n)!/(n!*2^(n-1)). 9
2, 2, 6, 30, 210, 1890, 20790, 270270, 4054050, 68918850, 1309458150, 27498621150, 632468286450, 15811707161250, 426916093353750, 12380566707258750, 383797567925021250, 12665319741525701250, 443286190953399543750, 16401589065275783118750, 639661973545755541631250 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Equals 2*A001147.

Also, the number of ways to paint the 2n cells of dimension n-1 that bound a regular convex n-cube polytope using exactly 2n colors where n > 0 is the dimension of Euclidean space. - Frank M Jackson, Aug 13 2018

REFERENCES

Right-hand edge of triangle in A097749.

LINKS

Muniru A Asiru, Table of n, a(n) for n = 0..150

Guo-Niu Han, Enumeration of Standard Puzzles [BROKEN LINK]

Guo-Niu Han, Enumeration of Standard Puzzles [Cached copy]

FORMULA

a(n) = 2*(2*n-1)!!. - Johannes W. Meijer, Nov 12 2009

E.g.f.: 2/sqrt(1-2*x). - Sergei N. Gladkovskii, Jul 06 2012

G.f.: G(0), where G(k)= 1 + 1/(1 - x*(2*k+1)/(x*(2*k+1) + 1/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, May 26 2013

a(n) = 2 * Product_{i=1..n} denominator( i!/(2i-1) ). - Wesley Ivan Hurt, Oct 12 2013

MAPLE

a:= proc(n) a(n):= `if`(n=0, 2, a(n-1)*(2*n-1)) end:

seq(a(n), n=0..25);  # Alois P. Heinz, May 27 2013

MATHEMATICA

FoldList[Times, 2, Range[1, 39, 2]] (* Arkadiusz Wesolowski, May 08 2012 *)

2(2*Range[0, 20]-1)!! (* Harvey P. Dale, Apr 22 2013 *)

CoefficientList[Series[2/Sqrt[1-2*x], {x, 0, 45}], x]*Table[k !, {k, 0, 45}] (* Stefano Spezia, Sep 04 2018 *)

PROG

(MAGMA) [Factorial(2*n)/(Factorial(n)*2^(n-1)): n in [0..20]]; // Vincenzo Librandi, Aug 21 2018

(GAP) List([0..20], n->Factorial(2*n)/(Factorial(n)*2^(n-1))); # Muniru A Asiru, Aug 21 2018

(PARI) x='x+O('x^30); Vec(serlaplace(2*(1-2*x)^(-1/2))) \\ Altug Alkan, Sep 05 2018

CROSSREFS

Appears in A167576. - Johannes W. Meijer, Nov 12 2009

Sequence in context: A278258 A067644 A184312 * A164347 A052584 A094303

Adjacent sequences:  A097798 A097799 A097800 * A097802 A097803 A097804

KEYWORD

nonn,changed

AUTHOR

N. J. A. Sloane, Sep 21 2004

STATUS

approved

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Last modified September 21 21:38 EDT 2018. Contains 315262 sequences. (Running on oeis4.)