A052768 - OEIS

%I #16 Jan 13 2025 09:07:00

%S 0,0,0,0,0,120,360,840,1680,3024,5040,7920,11880,17160,24024,32760,

%T 43680,57120,73440,93024,116280,143640,175560,212520,255024,303600,

%U 358800,421200,491400,570024,657720,755160,863040,982080,1113024

%N a(n) = n*(n-1)*(n-2*(n-3) for n>=5.

%C Old name was: A simple grammar.

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=725">Encyclopedia of Combinatorial Structures 725</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).

%F a(n)=0, n <= 4; a(n) = n*(n-1)*(n-2)*(n-3), n >= 5.

%F G.f.: 24*x^5*(5-10*x+10*x^2-5*x^3+x^4)/(1-x)^5. [_Colin Barker_, Jun 25 2012]

%p spec := [S,{B=Set(Z,1 <= card),S=Prod(Z,Z,Z,Z,B)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);

%Y Essentially the same as A052762.

%K easy,nonn

%O 0,6

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

%E More terms and corrected formula from Larry Reeves (larryr(AT)acm.org), Jan 23 2001