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 A007175 Number of simplicial 4-clusters with n cells. (Formerly M2762) 2
 1, 1, 1, 3, 8, 40, 211, 1406, 9754, 71591, 537699, 4131943, 32271490, 255690412, 2050376883, 16616721067, 135920429975, 1120999363012, 9313779465810, 77897862860818, 655433405297407, 5544948758579214, 47143948331898873, 402655164736641843, 3453509765971944236, 29734988097830504532 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Hering article has error in the 20th term. - Robert A. Russell, Apr 20 2012 REFERENCES F. Hering et al., The enumeration of stack polytopes and simplicial clusters, Discrete Math., 40 (1982), 203-217. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS MATHEMATICA Table[Binomial[4 n, n]/(12 (3 n + 1) (3 n + 2)) +   If[EvenQ[n],    Binomial[2 n, n/2]/(8 (3 n/2 + 1)) +     Binomial[2 n - 1, n/2 - 1]/((3 n/2 + 1)),    Binomial[2 n - 1, n/2 - 1/2]/(2 (3 n/2 + 1/2))] +   Switch[Mod[n, 3], 0, Binomial[4 n/3, n/3]/(3 (n + 1)), 1,    2 Binomial[4 n/3 - 1/3, n/3 - 1/3]/(3 (n + 1)), 2,    Binomial[4 n/3 - 2/3, n/3 - 2/3]/(n + 1)] +   If[2 == Mod[n, 4], Binomial[n - 1, n/4 - 1/2]/(2 (3 n/4 + 1/2)), 0] +   If[1 == Mod[n, 5], 2 Binomial[4 n/5 - 4/5, n/5 - 1/5]/(5 (3 n/5 + 2/5)),    0], {n, 1, 30}] (* Robert A. Russell, Apr 20 2012 *) CROSSREFS Sequence in context: A262126 A110561 A107991 * A152394 A168468 A224246 Adjacent sequences:  A007172 A007173 A007174 * A007176 A007177 A007178 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from Robert A. Russell, Apr 20 2012 STATUS approved

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Last modified December 6 14:15 EST 2019. Contains 329806 sequences. (Running on oeis4.)