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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)!.

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