A007816 Number of abstract simplicial 2-complexes on {1,2,3,...,n+3} which triangulate the 2-sphere: C(n+3,2)*(4n+1)!/(3n+3)!.

1, 10, 195, 5712, 223440, 10929600, 641277000, 43859692800, 3424685806080, 300495408595200, 29262949937020800, 3131187613956864000, 365112996737448960000, 46075561988281233408000

Offset

1,2

References

Foulds, L. R. Enumeration of graph theoretic solutions for facilities layout. Proceedings of the sixteenth Southeastern international conference on combinatorics, graph theory and computing (Boca Raton, Fla., 1985). Congr. Numer. 48 (1985), 87--99. MR0830702(87f:90045). See Table 2. - From N. J. A. Sloane, Apr 06 2012

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..200

William T. Tutte, A census of planar triangulations, Canad. J. Math. 14 (1962), 21-38.

Formula

a(n) ~ 2^(2+8*n)*3^(-7/2-3*n)*exp(-n)*n^n. - Stefano Spezia, Aug 03 2022

Maple

A007816:=n->binomial(n+3, 2)*(4*n+1)!/(3*n+3)!; seq(A007816(n), n=1..20);

Mathematica

Table[Binomial[n+3, 2] (4n+1)!/(3n+3)!, {n, 20}] (* Harvey P. Dale, May 16 2012 *)

Prog

(Magma) [Binomial(n+3, 2)*Factorial(4*n+1)/Factorial(3*n+3): n in [1..20]]; // Vincenzo Librandi, May 21 2012
(Python)
from math import factorial
def A007816(n): return ((n*(n + 5) + 6)*factorial((n<<2)+1)>>1)//factorial(3*(n+1)) # Chai Wah Wu, Nov 17 2022

Crossrefs

Sequence in context: A341503 A187652 A361311 * A365176 A126463 A239766

Adjacent sequences: A007813 A007814 A007815 * A007817 A007818 A007819

Keyword

nonn,easy,nice

Author

Victor Reiner (reiner(AT)math.umn.edu), Paul Edelman (edelman(AT)math.umn.edu)

Status

approved