A052731 - OEIS

%I #20 Nov 19 2021 07:49:27

%S 0,0,0,6,48,600,8640,151200,3064320,71124480,1857945600,54007430400,

%T 1729195776000,60483053030400,2294881337548800,93889711948032000,

%U 4120492394962944000,193100926276177920000,9624765220305371136000

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

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=687">Encyclopedia of Combinatorial Structures 687</a>

%F D-finite with recurrence: a(1)=0; a(2)=0; a(3)=6; (-15*n+15*n^3+15*n^2+3*n^4-18)*a(n) +(-n^3-7*n^2-16*n-12)*a(n+1) +(-3*n^2-16*n-21)*a(n+2) +(n+4)*a(n+3)=0; a(4)=48; a(5)=600.

%F Conjecture: a(n) = n!*A002026(n-2). - _R. J. Mathar_, Oct 16 2013

%F a(n) ~ sqrt(2) * 3^(n - 1/2) * n^(n-1) / exp(n). - _Vaclav Kotesovec_, Nov 19 2021

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

%K easy,nonn

%O 0,4

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