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%I M2762 #21 Jan 11 2020 18:33:58
%S 1,1,1,3,8,40,211,1406,9754,71591,537699,4131943,32271490,255690412,
%T 2050376883,16616721067,135920429975,1120999363012,9313779465810,
%U 77897862860818,655433405297407,5544948758579214,47143948331898873,402655164736641843,3453509765971944236,29734988097830504532
%N Number of simplicial 4-clusters with n cells.
%C Hering article has error in the 20th term. - _Robert A. Russell_, Apr 20 2012
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H F. Hering et al., <a href="http://dx.doi.org/10.1016/0012-365X(82)90121-2">The enumeration of stack polytopes and simplicial clusters</a>, Discrete Math., 40 (1982), 203-217.
%t Table[Binomial[4 n, n]/(12 (3 n + 1) (3 n + 2)) +
%t If[EvenQ[n],
%t Binomial[2 n, n/2]/(8 (3 n/2 + 1)) +
%t Binomial[2 n - 1, n/2 - 1]/((3 n/2 + 1)),
%t Binomial[2 n - 1, n/2 - 1/2]/(2 (3 n/2 + 1/2))] +
%t Switch[Mod[n, 3], 0, Binomial[4 n/3, n/3]/(3 (n + 1)), 1,
%t 2 Binomial[4 n/3 - 1/3, n/3 - 1/3]/(3 (n + 1)), 2,
%t Binomial[4 n/3 - 2/3, n/3 - 2/3]/(n + 1)] +
%t If[2 == Mod[n, 4], Binomial[n - 1, n/4 - 1/2]/(2 (3 n/4 + 1/2)), 0] +
%t If[1 == Mod[n, 5], 2 Binomial[4 n/5 - 4/5, n/5 - 1/5]/(5 (3 n/5 + 2/5)),
%t 0], {n, 1, 30}] (* _Robert A. Russell_, Apr 20 2012 *)
%K nonn,easy
%O 1,4
%A _N. J. A. Sloane_
%E More terms from _Robert A. Russell_, Apr 20 2012
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