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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 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS F. Hering et al., The enumeration of stack polytopes and simplicial clusters, Discrete Math., 40 (1982), 203-217. 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 A330527 Adjacent sequences:  A007172 A007173 A007174 * A007176 A007177 A007178 KEYWORD nonn,easy,changed AUTHOR EXTENSIONS More terms from Robert A. Russell, Apr 20 2012 STATUS approved

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Last modified January 21 21:30 EST 2020. Contains 331128 sequences. (Running on oeis4.)