A052694 - OEIS

%I #22 Jun 08 2022 03:27:40

%S 1,2,8,54,384,3840,46080,645120,10321920,185794560,3715891200,

%T 81749606400,1961990553600,51011754393600,1428329123020800,

%U 42849873690624000,1371195958099968000,46620662575398912000

%N Expansion of e.g.f. (1 + x^3 - 2*x^4)/(1-2*x).

%H G. C. Greubel, <a href="/A052694/b052694.txt">Table of n, a(n) for n = 0..350</a>

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=643">Encyclopedia of Combinatorial Structures 643</a>

%F E.g.f.: (1 + x^3 - 2*x^4)/(1-2*x).

%F D-finite Recurrence: a(0)=1, a(1)=2, a(2)=8, a(3)=54, a(4)=384, a(n) = 2*n*a(n-1).

%F a(n) = 2^n*n! + 6*[n=3].

%F G.f.: 6*x^3 + Hypergeometric2F0([1,1], [], 2*x). - _G. C. Greubel_, Jun 01 2022

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

%t With[{nn=20},CoefficientList[Series[(1+x^3-2x^4)/(1-2x),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Nov 12 2014 *)

%o (Magma) [n eq 3 select 54 else 2^n*Factorial(n): n in [0..30]]; // _G. C. Greubel_, Jun 01 2022

%o (SageMath) [2^n*factorial(n) + 6*bool(n==3) for n in (0..30)] # _G. C. Greubel_, Jun 01 2022

%Y Cf. A000079, A000142.

%K easy,nonn

%O 0,2

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