A005463 Number of simplices in barycentric subdivision of n-simplex. (Formerly M5326)

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

Offset

4,2

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R. Austin, R. K. Guy, and R. Nowakowski, unpublished notes, circa 1987.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R. Austin, R. K. Guy, and R. Nowakowski, Unpublished notes, 1987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

Formula

Essentially Stirling numbers of second kind - see A028246.

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

Prog

(Magma) [Factorial(n-4)*StirlingSecond(n+2, n-3): n in [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

Crossrefs

Cf. A005460, A005461, A005462, A005464, A005465.

Cf. A028246, A112494.

Sequence in context: A107319 A243214 A341569 * A160896 A017779 A110826

Adjacent sequences: A005460 A005461 A005462 * A005464 A005465 A005466

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Alois P. Heinz, Apr 27 2022

Status

approved