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 A052707 Odd powers of 2 multiplied by Catalan numbers. 2
 0, 2, 8, 64, 640, 7168, 86016, 1081344, 14057472, 187432960, 2549088256, 35223764992, 493132709888, 6979724509184, 99710350131200, 1435829041889280, 20819521107394560, 303720072625520640, 4454561065174302720 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS And/Or trees with 1 variable [Chauvin et al.]. - R. J. Mathar, Apr 01 2012 LINKS B. Chauvin, P. Flajolet et al., And/Or Tree Revisited, Combinat., Probal. Comput. 13 (2004) 475-497 INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 662 FORMULA a(n-1) = 2^(2*n+1)*A000108(n). Recurrence: a(1)=2, (-8+16*n)*a(n)-(n+1)*a(n+1) =0. a(n) = 16^n*(GAMMA(n-1/2)/(8*GAMMA(n+1)*Pi^(1/2))), n>0. 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)). 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); # 2nd program A052707 := proc(n)     if n =0 then         0;     else         2^(2*n-1)*A000108(n-1) ;     fi ; end proc: seq(A052707(n), n=0..10) ; # R. J. Mathar, Apr 26 2017 MATHEMATICA InverseSeries[Series[y/2-y^2, {y, 0, 24}], x] (* then A(x)=y(x) *) (* Len Smiley, Apr 13 2000 *) PROG (PARI) a(n)=if(n<1, 0, n--; 2*4^n*binomial(2*n, n)/(n+1)) CROSSREFS Sequence in context: A287229 A323853 A191570 * A059862 A268666 A193549 Adjacent sequences:  A052704 A052705 A052706 * A052708 A052709 A052710 KEYWORD easy,nonn AUTHOR encyclopedia(AT)pommard.inria.fr, Jan 25 2000 STATUS approved

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Last modified September 16 08:36 EDT 2019. Contains 327091 sequences. (Running on oeis4.)