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A052737 a(n) = ((2*n)!/n!)*2^(2*n+1). 0
0, 2, 16, 384, 15360, 860160, 61931520, 5449973760, 566797271040, 68015672524800, 9250131463372800, 1406019982432665600, 236211357048687820800, 43462889696958559027200, 8692577939391711805440000, 1877596834908609749975040000, 435602465698797461994209280000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A simple context-free grammar in a labeled universe.

LINKS

Table of n, a(n) for n=0..16.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 693

FORMULA

E.g.f.: 1/4-1/4*sqrt(1-16*x).

Recurrence: {a(1)=2, (8-16*n)*a(n)+a(n+1)}.

a(n) = (1/8)*16^(n+1)*GAMMA(n+1/2)/Pi^(1/2).

a(n) = n! * A052707(n). - R. J. Mathar, Aug 21 2014

MAPLE

spec := [S, {B=Union(Z, C), S=Union(B, Z, C), C=Prod(S, S)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);

[seq((2*n)!/n!*2^(2*n+1), n=0..12)]; - Zerinvary Lajos, Sep 28 2006

MATHEMATICA

With[{nn=20}, CoefficientList[Series[1/4-Sqrt[1-16x]/4, {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Aug 12 2015 *)

CROSSREFS

Cf. A052707.

Sequence in context: A068471 A140308 A280723 * A002474 A172149 A295710

Adjacent sequences:  A052734 A052735 A052736 * A052738 A052739 A052740

KEYWORD

easy,nonn

AUTHOR

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

EXTENSIONS

Better definition from Zerinvary Lajos, Sep 28 2006

More terms from Harvey P. Dale, Aug 12 2015

STATUS

approved

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Last modified March 19 00:14 EDT 2019. Contains 321306 sequences. (Running on oeis4.)