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A007816
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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)!.
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4
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1, 10, 195, 5712, 223440, 10929600, 641277000, 43859692800, 3424685806080, 300495408595200, 29262949937020800, 3131187613956864000, 365112996737448960000, 46075561988281233408000
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OFFSET
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1,2
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REFERENCES
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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
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LINKS
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FORMULA
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a(n) ~ 2^(2+8*n)*3^(-7/2-3*n)*exp(-n)*n^n. - Stefano Spezia, Aug 03 2022
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MAPLE
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A007816:=n->binomial(n+3, 2)*(4*n+1)!/(3*n+3)!; seq(A007816(n), n=1..20);
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MATHEMATICA
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Table[Binomial[n+3, 2] (4n+1)!/(3n+3)!, {n, 20}] (* Harvey P. Dale, May 16 2012 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,easy,nice
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AUTHOR
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Victor Reiner (reiner(AT)math.umn.edu), Paul Edelman (edelman(AT)math.umn.edu)
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STATUS
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approved
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