OFFSET
0,1
LINKS
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 561.
FORMULA
E.g.f.: (2*x+3)/(1-x^2).
Recurrence: {a(1)=2, a(0)=3, (-2-n^2-3*n)*a(n) + a(n+2) = 0}.
a(n) = Sum(1/2*(3*_alpha+2)*_alpha^(-1-n), _alpha=RootOf(-1+_Z^2))*n!.
a(n) = 3n! if n is even, 2n! otherwise.
a(n) = n!*A176059(n). - R. J. Mathar, Jun 03 2022
Sum_{n>=0} 1/a(n) = (5*e^2-1)/(12*e) = cosh(1)/3 + sinh(1)/2. - Amiram Eldar, Feb 02 2023
MAPLE
spec := [S, {S=Union(Sequence(Z), Sequence(Z), Sequence(Prod(Z, Z)))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
MATHEMATICA
With[{nn=30}, CoefficientList[Series[(3+2x)/(1-x^2), {x, 0, nn}], x] Range[ 0, nn]!] (* Harvey P. Dale, Dec 12 2021 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
STATUS
approved