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E.g.f. [1 -3x -sqrt(1-6x+x^2) -x*(1-x-sqrt(1-6x+x^2)) ]/2.
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%I #23 Jan 30 2020 21:29:14

%S 0,0,2,24,384,8160,218880,7116480,272240640,11985200640,596981145600,

%T 33195609216000,2038500521164800,137021183973273600,

%U 10006412139653529600,788930789450259456000,66790064645111808000000,6042970648669883056128000,581917311773908793819136000,59423732260666221275283456000

%N E.g.f. [1 -3x -sqrt(1-6x+x^2) -x*(1-x-sqrt(1-6x+x^2)) ]/2.

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=692">Encyclopedia of Combinatorial Structures 692</a>

%F D-finite with recurrence: a(1)=0; a(2)=2; a(3)=24; (-n^3-n^2+4*n+4)*a(n) +(-6+7*n^2+11*n)*a(n+1) +(-7*n-10)*a(n+2) +a(n+3) =0.

%F a(n) ~ (2-sqrt(2))*sqrt(3*sqrt(2)-4)*n^(n-1)*(3+2*sqrt(2))^n/exp(n). - _Vaclav Kotesovec_, Oct 05 2013

%F Conjecture: a(n) = n!*A006319(n-1). - _R. J. Mathar_, Oct 16 2013

%p spec := [S,{B=Prod(Z,C),S=Prod(C,C),C=Union(B,S,Z)},labeled]: seq(combstruct[count](spec,size=n), n=0..20); # end of program

%p 0, seq(simplify( n!*(n-1)*hypergeom([n, 2-n],[3],-1) ), n=1..20); # _Mark van Hoeij_, May 29 2013

%t CoefficientList[Series[1/2-3/2*x-1/2*(1-6*x+x^2)^(1/2)-(1/2-1/2*x-1/2*(1-6*x+x^2)^(1/2))*x, {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Oct 05 2013 *)

%o (PARI) x='x+O('x^66); concat([0,0], Vec( serlaplace( 1/2-3/2*x -1/2*(1-6*x+x^2)^(1/2) -(1/2-1/2*x-1/2*(1-6*x+x^2)^(1/2))*x))) \\ _Joerg Arndt_, May 29 2013

%K easy,nonn

%O 0,3

%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000