login
A052694
Expansion of e.g.f. (1 + x^3 - 2*x^4)/(1-2*x).
1
1, 2, 8, 54, 384, 3840, 46080, 645120, 10321920, 185794560, 3715891200, 81749606400, 1961990553600, 51011754393600, 1428329123020800, 42849873690624000, 1371195958099968000, 46620662575398912000
OFFSET
0,2
LINKS
FORMULA
E.g.f.: (1 + x^3 - 2*x^4)/(1-2*x).
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).
a(n) = 2^n*n! + 6*[n=3].
G.f.: 6*x^3 + Hypergeometric2F0([1,1], [], 2*x). - G. C. Greubel, Jun 01 2022
MAPLE
spec := [S, {S=Union(Sequence(Union(Z, Z)), Prod(Z, Z, Z))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
MATHEMATICA
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 *)
PROG
(Magma) [n eq 3 select 54 else 2^n*Factorial(n): n in [0..30]]; // G. C. Greubel, Jun 01 2022
(SageMath) [2^n*factorial(n) + 6*bool(n==3) for n in (0..30)] # G. C. Greubel, Jun 01 2022
CROSSREFS
Sequence in context: A197931 A296788 A079503 * A069729 A346647 A354690
KEYWORD
easy,nonn
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
STATUS
approved