cp's OEIS Frontend

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

%I A005463 M5326 #27 Nov 23 2022 08:57:57
%S A005463 1,63,1932,46620,1020600,21538440,451725120,9574044480,207048441600,
%T A005463 4595022432000,105006251750400,2475732702643200,60284572969420800,
%U A005463 1516762345722624000,39433286715863040000,1059143615076298752000,29378569022287220736000,841159994641469927424000
%N A005463 Number of simplices in barycentric subdivision of n-simplex.
%D A005463 R. Austin, R. K. Guy, and R. Nowakowski, unpublished notes, circa 1987.
%D A005463 R. K. Guy, personal communication.
%D A005463 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A005463 G. C. Greubel, <a href="/A005463/b005463.txt">Table of n, a(n) for n = 4..440</a>
%H A005463 R. Austin, R. K. Guy, and R. Nowakowski, <a href="/A000629/a000629.pdf">Unpublished notes, 1987</a>
%H A005463 Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Enumerative Formulas for Some Functions on Finite Sets</a>
%H A005463 Rajesh Kumar Mohapatra and Tzung-Pei Hong, <a href="https://doi.org/10.3390/math10071161">On the Number of Finite Fuzzy Subsets with Analysis of Integer Sequences</a>, Mathematics (2022) Vol. 10, No. 7, 1161.
%F A005463 Essentially Stirling numbers of second kind - see A028246.
%F A005463 a(n) = (n-4)! * Stirling2(n+2, n-3). - _Alois P. Heinz_, Apr 27 2022
%p A005463 a:= n-> Stirling2(2+n,n-3)*(n-4)!:
%p A005463 seq(a(n), n=4..21);  # _Alois P. Heinz_, Apr 27 2022
%t A005463 Table[(n-4)!*StirlingS2[n+2, n-3], {n,4,35}] (* _G. C. Greubel_, Nov 22 2022 *)
%o A005463 (Magma) [Factorial(n-4)*StirlingSecond(n+2,n-3): n in [4..35]]; // _G. C. Greubel_, Nov 22 2022
%o A005463 (SageMath) [factorial(n-4)*stirling_number2(n+2,n-3) for n in range(4,36)] # _G. C. Greubel_, Nov 22 2022
%Y A005463 Cf. A005460, A005461, A005462, A005464, A005465.
%Y A005463 Cf. A028246, A112494.
%K A005463 nonn
%O A005463 4,2
%A A005463 _N. J. A. Sloane_
%E A005463 More terms from _Alois P. Heinz_, Apr 27 2022