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A005464 Number of simplices in barycentric subdivision of n-simplex.

%I A005464 M5391 #27 Nov 23 2022 08:57:50
%S A005464 1,127,6050,204630,5921520,158838240,4115105280,105398092800,
%T A005464 2706620716800,70309810771200,1858166876966400,50148628078348800,
%U A005464 1385482985542656000,39245951652171264000,1140942623868343296000,34060437199245929472000,1044402668566817624064000,32895725269182358302720000
%N A005464 Number of simplices in barycentric subdivision of n-simplex.
%D A005464 R. Austin, R. K. Guy, and R. Nowakowski, unpublished notes, circa 1987.
%D A005464 R. K. Guy, personal communication.
%D A005464 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A005464 G. C. Greubel, <a href="/A005464/b005464.txt">Table of n, a(n) for n = 5..440</a>
%H A005464 R. Austin, R. K. Guy, and R. Nowakowski, <a href="/A000629/a000629.pdf">Unpublished notes, 1987</a>
%H A005464 Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Enumerative Formulas for Some Functions on Finite Sets</a>
%H A005464 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 A005464 Essentially Stirling numbers of second kind - see A028246.
%F A005464 a(n) = (n-5)! * Stirling2(n+2, n-4). - _G. C. Greubel_, Nov 22 2022
%p A005464 seq((d+2)!*(63*d^5-945*d^4+5355*d^3-13951*d^2+15806*d-5304)/2903040,d=5..30) ; # _R. J. Mathar_, Mar 19 2018
%t A005464 Table[(n-5)!*StirlingS2[n+2, n-4], {n,5,35}] (* _G. C. Greubel_, Nov 22 2022 *)
%o A005464 (Magma) [Factorial(n-5)*StirlingSecond(n+2,n-4): n in [5..35]]; // _G. C. Greubel_, Nov 22 2022
%o A005464 (SageMath) [factorial(n-5)*stirling_number2(n+2,n-4) for n in range(5,36)] # _G. C. Greubel_, Nov 22 2022
%Y A005464 Cf. A005460, A005461, A005462, A005463, A005465.
%Y A005464 Cf. A028246, A144969.
%K A005464 nonn,easy
%O A005464 5,2
%A A005464 _N. J. A. Sloane_