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A001763
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Number of dissections of a ball: (3n+3)!/(2n+3)!.
(Formerly M4279 N1788)
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4
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1, 1, 6, 72, 1320, 32760, 1028160, 39070080, 1744364160, 89513424000, 5191778592000, 335885501952000, 23982224839372800, 1873278229119897600, 158905670470170624000, 14547557832075620352000
(list; graph; refs; listen; history; internal format)
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OFFSET
| -1,3
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REFERENCES
| L. W. Beineke and R. E. Pippert, Enumerating labeled k-dimensional trees and ball dissections, pp. 12-26 of Proceedings of Second Chapel Hill Conference on Combinatorial Mathematics and Its Applications, University of North Carolina, Chapel Hill, 1970. Reprinted in Math. Annalen, 191 (1971), 87-98.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 407
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FORMULA
| E.g.f.: A(x)=(2/sqrt(3*x))*sin(arcsin(3*sqrt(3*x)/2)/3)=1+6*x/(Q(0)-6*x); Q(k)=3*x*(3*k+1)*(3*k+2)+2*(2*(k^2)+5*k+3)-6*x*(2*(k^2)+5*k+3)*(3*k+4)*(3*k+5)/Q(k+1) ; (continued fraction). - Sergei N. Gladkovskii, Nov 27 2011
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CROSSREFS
| Cf. A001762.
Sequence in context: A063965 A047058 A202382 * A003235 A113133 A089252
Adjacent sequences: A001760 A001761 A001762 * A001764 A001765 A001766
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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