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

1, 127, 6050, 204630, 5921520, 158838240, 4115105280, 105398092800, 2706620716800, 70309810771200, 1858166876966400, 50148628078348800, 1385482985542656000, 39245951652171264000, 1140942623868343296000, 34060437199245929472000, 1044402668566817624064000, 32895725269182358302720000

Offset: 5

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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• R. Austin, R. K. Guy, and R. Nowakowski, unpublished notes, circa 1987.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

• G. C. Greubel, Table of n, a(n) for n = 5..440
• R. Austin, R. K. Guy, and R. Nowakowski, Unpublished notes, 1987
• Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
• 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.

Crossrefs

Cf. A005460, A005461, A005462, A005463, A005465.

Cf. A028246, A144969.

Programs

Magma

[Factorial(n-5)*StirlingSecond(n+2,n-4): n in [5..35]]; // G. C. Greubel, Nov 22 2022

Maple

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

Mathematica

Table[(n-5)!*StirlingS2[n+2, n-4], {n,5,35}] (* G. C. Greubel, Nov 22 2022 *)

SageMath

[factorial(n-5)*stirling_number2(n+2,n-4) for n in range(5,36)] # G. C. Greubel, Nov 22 2022

Formula

Essentially Stirling numbers of second kind - see A028246.

a(n) = (n-5)! * Stirling2(n+2, n-4). - G. C. Greubel, Nov 22 2022