|
|
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
|
|
|
FORMULA
|
E.g.f.: 1/4 - (1/4)*sqrt(1-16*x).
D-finite Recurrence: {a(1)=2, (8-16*n)*a(n) + a(n+1)=0}.
a(n) = (1/8)*16^(n+1)*Gamma(n+1/2)/Pi^(1/2).
Sum_{n>=1} 1/a(n) = sqrt(Pi)*exp(1/16)*erf(1/4)/8, where erf is the error function.
Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(Pi)*exp(-1/16)*erfi(1/4)/8, where erfi is the imaginary error function. (End)
|
|
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);
|
|
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
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|