A005462 Number of simplices in barycentric subdivision of n-simplex.

1, 31, 602, 10206, 166824, 2739240, 46070640, 801496080, 14495120640, 273158645760, 5368729766400, 110055327782400, 2351983118284800, 52361635508582400, 1213240925049753600, 29227769646147072000, 731310069474496512000, 18984684514588176384000

Offset: 3

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• R. Austin, R. K. Guy, and R. Nowakowski, unpublished notes, circa 1987.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

• Micah Manary, Table of n, a(n) for n = 3..138
• R. Austin, R. K. Guy, and R. Nowakowski, Unpublished notes, 1987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.

Crossrefs

Cf. A001298, A005460, A005461, A028246.

Programs

Magma

[Factorial(n-3)*StirlingSecond(n+2,n-2): n in [3..30]]; // G. C. Greubel, Nov 22 2022

Mathematica

Table[(n-3)!*StirlingS2[n+2,n-2], {n,3,30}] (* G. C. Greubel, Nov 22 2022 *)

SageMath

[factorial(n-3)*stirling_number2(n+2,n-2) for n in range(3,31)] # G. C. Greubel, Nov 22 2022

Formula

Essentially Stirling numbers of second kind - see A028246.

a(n) = Stirling2(n+2,n-2)*(n-3)!. - Alois P. Heinz, Aug 28 2022