A005464 Number of simplices in barycentric subdivision of n-simplex. (Formerly M5391)

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

Offset

5,2

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R. Austin, R. K. Guy, and R. Nowakowski, unpublished notes, circa 1987.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

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R. Austin, R. K. Guy, and R. Nowakowski, Unpublished notes, 1987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.

Formula

Essentially Stirling numbers of second kind - see A028246.

a(n) = (n-5)! * Stirling2(n+2, n-4). - 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 *)

Prog

(Magma) [Factorial(n-5)*StirlingSecond(n+2, n-4): n in [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

Crossrefs

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

Cf. A028246, A144969.

Sequence in context: A201071 A137789 A268663 * A160898 A140477 A110828

Adjacent sequences: A005461 A005462 A005463 * A005465 A005466 A005467

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved