A005463 Number of simplices in barycentric subdivision of n-simplex.

1, 63, 1932, 46620, 1020600, 21538440, 451725120, 9574044480, 207048441600, 4595022432000, 105006251750400, 2475732702643200, 60284572969420800, 1516762345722624000, 39433286715863040000, 1059143615076298752000, 29378569022287220736000, 841159994641469927424000

Offset: 4

Author

N. J. A. Sloane

Keywords

• nonn

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• R. Austin, R. K. Guy, and R. Nowakowski, unpublished notes, circa 1987.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 = 4..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• R. Austin, R. K. Guy, and R. Nowakowski, Unpublished notes, 1987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, A005464, A005465.

Cf. A028246, A112494.

Programs

Magma

[Factorial(n-4)*StirlingSecond(n+2,n-3): n in [4..35]]; // G. C. Greubel, Nov 22 2022

Maple

a:= n-> Stirling2(2+n,n-3)*(n-4)!:
seq(a(n), n=4..21);  # Alois P. Heinz, Apr 27 2022

Mathematica

Table[(n-4)!*StirlingS2[n+2, n-3], {n,4,35}] (* G. C. Greubel, Nov 22 2022 *)

SageMath

[factorial(n-4)*stirling_number2(n+2,n-3) for n in range(4,36)] # G. C. Greubel, Nov 22 2022

Formula

Essentially Stirling numbers of second kind - see A028246.

a(n) = (n-4)! * Stirling2(n+2, n-3). - Alois P. Heinz, Apr 27 2022

Extensions

More terms from Alois P. Heinz, Apr 27 2022