OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..375
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 645
FORMULA
E.g.f.: (1 - x)^2/(1 - 4*x + 3*x^2 - x^3).
D-finite recurrence: a(0)=1, a(1)=2, a(2)=12, a(n) = 2*n*a(n-1) - 3*n*(n-1)*a(n-2) + n*(n-1)*(n-2)*a(n-3).
a(n) = n! * Sum_{alpha=RootOf(-1 +4*Z -3*Z^2 +Z^3)} (1/31)*(4 + 7*alpha - 2*alpha^2)*alpha^(-1-n).
a(n) = n! * A052544(n). - G. C. Greubel, May 31 2022
MAPLE
spec := [S, {S=Sequence(Union(Z, Prod(Z, Sequence(Z), Sequence(Z))))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
MATHEMATICA
With[{nn=20}, CoefficientList[Series[(1-x)^2/(1-4x+3x^2-x^3), {x, 0, nn}], x]Range[0, nn]!] (* Harvey P. Dale, Aug 28 2012 *)
PROG
(Magma) R<x>:=PowerSeriesRing(Rationals(), 30);
Coefficients(R!(Laplace( (1-x)^2/(1-4*x+3*x^2-x^3) ))); // G. C. Greubel, May 31 2022
(SageMath)
@CachedFunction
def b(n): # b = A052544
if (n<3): return factorial(n+1)
else: return 4*b(n-1) - 3*b(n-2) + b(n-3)
def A052696(n): return factorial(n)*b(n)
[A052696(n) for n in (0..40)] # G. C. Greubel, May 31 2022
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
STATUS
approved