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A005463
Number of simplices in barycentric subdivision of n-simplex.
(Formerly M5326)
5
1, 63, 1932, 46620, 1020600, 21538440, 451725120, 9574044480, 207048441600, 4595022432000, 105006251750400, 2475732702643200, 60284572969420800, 1516762345722624000, 39433286715863040000, 1059143615076298752000, 29378569022287220736000, 841159994641469927424000
OFFSET
4,2
REFERENCES
R. Austin, R. K. Guy, and R. Nowakowski, unpublished notes, circa 1987.
R. K. Guy, personal communication.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
R. Austin, R. K. Guy, and R. Nowakowski, Unpublished notes, 1987
Rajesh Kumar Mohapatra and Tzung-Pei Hong, On the Number of Finite Fuzzy Subsets with Analysis of Integer Sequences, Mathematics (2022) Vol. 10, No. 7, 1161.
FORMULA
Essentially Stirling numbers of second kind - see A028246.
a(n) = (n-4)! * Stirling2(n+2, n-3). - Alois P. Heinz, Apr 27 2022
MAPLE
a:= n-> Stirling2(2+n, n-3)*(n-4)!:
seq(a(n), n=4..21); # Alois P. Heinz, Apr 27 2022
MATHEMATICA
Table[(n-4)!*StirlingS2[n+2, n-3], {n, 4, 35}] (* G. C. Greubel, Nov 22 2022 *)
PROG
(Magma) [Factorial(n-4)*StirlingSecond(n+2, n-3): n in [4..35]]; // G. C. Greubel, Nov 22 2022
(SageMath) [factorial(n-4)*stirling_number2(n+2, n-3) for n in range(4, 36)] # G. C. Greubel, Nov 22 2022
CROSSREFS
KEYWORD
nonn
EXTENSIONS
More terms from Alois P. Heinz, Apr 27 2022
STATUS
approved