OFFSET
0,2
COMMENTS
With a(n)=1, also number of labeled mobiles with n nodes and 2-colored internal (non-leaf) nodes - Christian G. Bower, Jun 07 2005
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..345
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 672
FORMULA
D-finite with recurrence: a(2)=4, a(1)=2, (n^2-1)*a(n) = (3+6*n)*a(n+1) - a(n+2).
a(n) = n!*A006318(n-1), n>=2. - R. J. Mathar, Oct 26 2013
MAPLE
spec := [S, {C=Union(B, Z), B=Prod(S, C), S=Union(Z, C)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
MATHEMATICA
With[{nn=20}, CoefficientList[Series[(x+1-Sqrt[1-6x+x^2])/2, {x, 0, nn}], x] Range[ 0, nn]!] (* Harvey P. Dale, Apr 19 2020 *)
PROG
(Magma) [n le 1 select 1-(-1)^n else Factorial(n)*(&+[Catalan(k)*Binomial(n+k-1, n-k-1): k in [0..n-1]]): n in [0..30]]; // G. C. Greubel, May 28 2022
(SageMath) [bool(n==1)+factorial(n)*sum(binomial(n+k-1, n-k-1)*catalan_number(k) for k in (0..n-1)) for n in (0..30)] # G. C. Greubel, May 28 2022
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
STATUS
approved