|
Search: id:A052707
|
|
|
| A052707 |
|
A simple context-free grammar. |
|
+0
1
|
|
| 0, 2, 8, 64, 640, 7168, 86016, 1081344, 14057472, 187432960, 2549088256, 35223764992, 493132709888, 6979724509184, 99710350131200, 1435829041889280, 20819521107394560, 303720072625520640, 4454561065174302720
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
LINKS
|
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 662
|
|
FORMULA
|
Recurrence: {a(1)=2, (-8+16*n)*a(n)-(n+1)*a(n+1)}
(1/8)*GAMMA(n+1/2)/(GAMMA(n+2)*Pi^(1/2)*16^(n+1))
Given g.f. A(x), then B(x)=A(x)-x series reversion is -B(-x). - Michael Somos Sep 08 2005
Given g.f. A(x), then B(x)=A(x)-x satisfies B(x)=x+8*C(16*x*B(x)) where C(x) is g.f. for Catalan number A000108.
G.f. A(x) = 2*x*C(4*x) where C(x) is g.f. for Catalan number A000108.
G.f.: (1-sqrt(1-16*x))/4 = (4*x)/(1+sqrt(1-16*x)). a(n-1)=2^(2n+1)c(n) where c(n) is Catalan numbers A000108.
|
|
MAPLE
|
spec := [S, {C=Union(B, Z), B=Prod(S, S), S=Union(B, C, Z)}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..20);
|
|
MATHEMATICA
|
InverseSeries[Series[y/2-y^2, {y, 0, 24}], x] (* then A(x)=y(x) *) - Len Smiley Apr 13 2000
|
|
PROGRAM
|
(PARI) a(n)=if(n<1, 0, n--; 2*4^n*binomial(2*n, n)/(n+1))
|
|
CROSSREFS
|
Sequence in context: A153526 A153554 A139018 this_sequence A059862 A005612 A136282
Adjacent sequences: A052704 A052705 A052706 this_sequence A052708 A052709 A052710
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
|
|
|
Search completed in 0.002 seconds
|
