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A181914 Number of And/Or trees with n internal nodes that compute the Boolean value True. 1
2, 16, 168, 1920, 23360, 296448, 3880576, 52015104, 710360064, 9849036800, 138270871552, 1961643540480, 28079294676992, 405035709890560, 5881791327928320, 85917550984036352, 1261588096997916672, 18611082818941353984 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..200

B. Chauvin, P. Flajolet, et al., And/Or Tree Revisited, Combinat., Probal. Comput. 13 (2004) 475-497

FORMULA

G.f.: (2-sqrt(2+16*x+2*sqrt(1-16*x)))/(8*x).

Recurrence: (n+1)*(2*n+1)*a(n) = 12*n*(3*n-1)*a(n-1) - 48*(n^2-5*n+5)*a(n-2) - 128*(n-2)*(2*n-5)*a(n-3). - Vaclav Kotesovec, Oct 20 2012

a(n) ~ 16^n/(sqrt(3*Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 20 2012

MAPLE

g := (2-sqrt(2+16*z+2*sqrt(1-16*z)))/8/z ; seq(coeftayl(%, z=0, n), n=1..20) ;

MATHEMATICA

Rest[CoefficientList[Series[(2-Sqrt[2+16*x+2*Sqrt[1-16*x]])/(8*x), {x, 0, 20}], x]] (* Vaclav Kotesovec, Oct 20 2012 *)

CROSSREFS

Sequence in context: A219397 A275912 A337870 * A089624 A217804 A217799

Adjacent sequences:  A181911 A181912 A181913 * A181915 A181916 A181917

KEYWORD

nonn

AUTHOR

R. J. Mathar, Apr 01 2012

STATUS

approved

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Last modified October 23 04:06 EDT 2021. Contains 348211 sequences. (Running on oeis4.)