A052587 - OEIS

%I #20 Nov 11 2024 22:42:08

%S 0,0,2,6,48,480,5760,80640,1290240,23224320,464486400,10218700800,

%T 245248819200,6376469299200,178541140377600,5356234211328000,

%U 171399494762496000,5827582821924864000,209792981589295104000

%N Expansion of e.g.f. x^2*(1-x)/(1-2*x).

%C Essentially the same as A051578. - _R. J. Mathar_, Feb 22 2008

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=532">Encyclopedia of Combinatorial Structures 532</a>

%F E.g.f.: x^2*(-1+x)/(-1+2*x).

%F Recurrence: a(0) = a(1) = 0, a(2) = 2, a(3) = 6, a(n+1) = 2*(n+1)*a(n) for n > 3.

%F a(n) = 1/8*2^n*n!, n > 2.

%F a(n) = A051578(n-2) = (2*n)!!/4!! for n > 2. - _M. F. Hasler_, Nov 10 2024

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

%o (PARI) apply( {A052587(n)=n!<<(n-3)+(n==2)}, [0..19]) \\ _M. F. Hasler_, Nov 10 2024

%Y Cf. A051578 (essentially the same), A000165 (double factorial), A000142 (factorial), A000079 (powers of 2).

%K easy,nonn

%O 0,3

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