A283049 Numbers of configurations of A'Campo forests with co-dimension 1 and degree n>0.

0, 4, 48, 480, 4560, 42504, 393120, 3624768, 33390720, 307618740, 2835722032, 26162863584, 241614915360, 2233533229200, 20667453710400, 191422799835264, 1774573628661504, 16465220088660432, 152894968403313600, 1420856831349155200, 13213537097286612240

Offset

0,2

Comments

We can prove this using generating functions. a(n) is given also by 4*binomial(4n,n-2), for n>1.

Links

Indranil Ghosh, Table of n, a(n) for n = 0..500

N. Combe, V. Jugé, Counting bi-colored A'Campo forests, arXiv:1702.07672 [math.AG], 2017.

Formula

a(n) = 4*binomial(4n,n-2), for n>1.

Example

For n=2 the a(2)=4 solutions are the number of A'Campo forests with co-dimension 1 and degree 2.

Mathematica

Table[4*Binomial[4n, n-2], {n, 1, 23}] (* Indranil Ghosh, Feb 28 2017 *)

Prog

(PARI) a(n) = 4*binomial(4*n, n-2) \\ Indranil Ghosh, Feb 28 2017

Crossrefs

Sequence in context: A299603 A026942 A264727 * A159903 A099671 A196963

Adjacent sequences: A283046 A283047 A283048 * A283050 A283051 A283052

Keyword

nonn

Author

Noemie Combe, Feb 27 2017

Status

approved