A181914 Number of And/Or trees with n internal nodes that compute the Boolean value True.

2, 16, 168, 1920, 23360, 296448, 3880576, 52015104, 710360064, 9849036800, 138270871552, 1961643540480, 28079294676992, 405035709890560, 5881791327928320, 85917550984036352, 1261588096997916672, 18611082818941353984

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