|
%I #32 Nov 17 2022 09:19:34
%S 1,10,195,5712,223440,10929600,641277000,43859692800,3424685806080,
%T 300495408595200,29262949937020800,3131187613956864000,
%U 365112996737448960000,46075561988281233408000
%N 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)!.
%D 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
%H Vincenzo Librandi, <a href="/A007816/b007816.txt">Table of n, a(n) for n = 1..200</a>
%H William T. Tutte, <a href="https://doi.org/10.4153/CJM-1962-002-9">A census of planar triangulations</a>, Canad. J. Math. 14 (1962), 21-38.
%F a(n) ~ 2^(2+8*n)*3^(-7/2-3*n)*exp(-n)*n^n. - _Stefano Spezia_, Aug 03 2022
%p A007816:=n->binomial(n+3,2)*(4*n+1)!/(3*n+3)!; seq(A007816(n), n=1..20);
%t Table[Binomial[n+3,2] (4n+1)!/(3n+3)!,{n,20}] (* _Harvey P. Dale_, May 16 2012 *)
%o (Magma) [Binomial(n+3, 2)*Factorial(4*n+1)/Factorial(3*n+3): n in [1..20]]; // _Vincenzo Librandi_, May 21 2012
%o (Python)
%o from math import factorial
%o def A007816(n): return ((n*(n + 5) + 6)*factorial((n<<2)+1)>>1)//factorial(3*(n+1)) # _Chai Wah Wu_, Nov 17 2022
%K nonn,easy,nice
%O 1,2
%A Victor Reiner (reiner(AT)math.umn.edu), Paul Edelman (edelman(AT)math.umn.edu)
|
