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A052707
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A simple context-free grammar.
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0
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0, 2, 8, 64, 640, 7168, 86016, 1081344, 14057472, 187432960, 2549088256, 35223764992, 493132709888, 6979724509184, 99710350131200, 1435829041889280, 20819521107394560, 303720072625520640, 4454561065174302720
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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LINKS
| INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 662
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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.
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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);
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MATHEMATICA
| InverseSeries[Series[y/2-y^2, {y, 0, 24}], x] (* then A(x)=y(x) *) - Len Smiley Apr 13 2000
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PROG
| (PARI) a(n)=if(n<1, 0, n--; 2*4^n*binomial(2*n, n)/(n+1))
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CROSSREFS
| Sequence in context: A139018 A110708 A191570 * A059862 A193549 A005612
Adjacent sequences: A052704 A052705 A052706 * A052708 A052709 A052710
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KEYWORD
| easy,nonn
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AUTHOR
| encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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