%I M5225 #34 Nov 23 2022 08:57:53
%S 1,31,602,10206,166824,2739240,46070640,801496080,14495120640,
%T 273158645760,5368729766400,110055327782400,2351983118284800,
%U 52361635508582400,1213240925049753600,29227769646147072000,731310069474496512000,18984684514588176384000
%N Number of simplices in barycentric subdivision of n-simplex.
%D R. Austin, R. K. Guy, and R. Nowakowski, unpublished notes, circa 1987.
%D R. K. Guy, personal communication.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Micah Manary, <a href="/A005462/b005462.txt">Table of n, a(n) for n = 3..138</a>
%H R. Austin, R. K. Guy, and R. Nowakowski, <a href="/A000629/a000629.pdf">Unpublished notes, 1987</a>
%H Rajesh Kumar Mohapatra and Tzung-Pei Hong, <a href="https://doi.org/10.3390/math10071161">On the Number of Finite Fuzzy Subsets with Analysis of Integer Sequences</a>, Mathematics (2022) Vol. 10, No. 7, 1161.
%F Essentially Stirling numbers of second kind - see A028246.
%F a(n) = Stirling2(n+2,n-2)*(n-3)!. - _Alois P. Heinz_, Aug 28 2022
%t Table[(n-3)!*StirlingS2[n+2,n-2], {n,3,30}] (* _G. C. Greubel_, Nov 22 2022 *)
%o (Magma) [Factorial(n-3)*StirlingSecond(n+2,n-2): n in [3..30]]; // _G. C. Greubel_, Nov 22 2022
%o (SageMath) [factorial(n-3)*stirling_number2(n+2,n-2) for n in range(3,31)] # _G. C. Greubel_, Nov 22 2022
%Y Cf. A001298, A005460, A005461, A028246.
%K nonn,easy
%O 3,2
%A _N. J. A. Sloane_