A052731 E.g.f. [1-x -sqrt(1-2x-3x^2)]/(2x) - [1+x-sqrt(1-2x-3x^2)]/2 .
0, 0, 0, 6, 48, 600, 8640, 151200, 3064320, 71124480, 1857945600, 54007430400, 1729195776000, 60483053030400, 2294881337548800, 93889711948032000, 4120492394962944000, 193100926276177920000, 9624765220305371136000
Offset: 0
Links
- INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 687
Programs
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Maple
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);
Formula
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.
Conjecture: a(n) = n!*A002026(n-2). - R. J. Mathar, Oct 16 2013
a(n) ~ sqrt(2) * 3^(n - 1/2) * n^(n-1) / exp(n). - Vaclav Kotesovec, Nov 19 2021