A005462 Number of simplices in barycentric subdivision of n-simplex. (Formerly M5225)

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

Offset

3,2

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R. Austin, R. K. Guy, and R. Nowakowski, unpublished notes, circa 1987.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

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R. Austin, R. K. Guy, and R. Nowakowski, Unpublished notes, 1987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

Formula

Essentially Stirling numbers of second kind - see A028246.

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

Mathematica

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

Prog

(Magma) [Factorial(n-3)*StirlingSecond(n+2, n-2): n in [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

Crossrefs

Cf. A001298, A005460, A005461, A028246.

Sequence in context: A022755 A003533 A360761 * A028201 A028184 A215794

Adjacent sequences: A005459 A005460 A005461 * A005463 A005464 A005465

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved