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A093197
Number of labeled plane 2-trees on n triangles.
2
1, 6, 56, 720, 11880, 240240, 5765760, 160392960, 5079110400, 180503769600, 7117005772800, 308403583488000, 14572069319808000, 745747076954880000, 41098950018846720000, 2427001153744527360000, 152901072685905223680000
OFFSET
2,2
LINKS
G. Labelle, C. Lamathe and P. Leroux, A classification of plane and planar 2-trees, arXiv:math/0202052 [math.CO], 2002.
FORMULA
a(n) = n! * (2/3 * C(n) - 1/6 * C(n+1)), where C(n) = A000108(n).
a(n) = RisingFactorial(5 + n, n) assuming offset 0. - Peter Luschny, Mar 22 2022
MATHEMATICA
a[n_]:=n! * (2/3 * CatalanNumber[n] - 1/6 * CatalanNumber[n+1]); Array[a, 50, 2] (* Stefano Spezia, Sep 01 2018 *)
PROG
(PARI) a(n)=if(n < 2, 0, n!*(4*binomial(2*n, n)/(n+1)-binomial(2*n+2, n+1)/(n+2))/6) \\ Andrew Howroyd, Aug 31 2018
CROSSREFS
Sequence in context: A290788 A215507 A112699 * A303921 A052317 A185524
KEYWORD
nonn
AUTHOR
Ralf Stephan, Apr 22 2004
STATUS
approved