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A001762
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Number of dissections of a ball.
(Formerly M4741 N2029)
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3
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1, 1, 10, 180, 4620, 152880, 6168960, 293025600, 15990004800, 984647664000, 67493121696000, 5094263446272000, 419688934689024000, 37465564582397952000, 3601861863990534144000, 370962724717928318976000, 40744403224500159055872000
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OFFSET
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3,3
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REFERENCES
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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
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T. D. Noe, Table of n, a(n) for n = 3..100
L. W. Beineke and R. E. Pippert, The Number of Labeled Dissections of a k-Ball., Math. Annalen, 191 (1971), 87-98.
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FORMULA
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a(n) = binomial(n,3)*(3*n-9)!/(2*n-4)!, n >= 4; a(3) = 1.
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MATHEMATICA
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Join[{1}, Table[Binomial[n, 3]*(3*n - 9)!/(2*n - 4)!, {n, 4, 25}]] (* T. D. Noe, Aug 10 2012 *)
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CROSSREFS
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Cf. A001763.
Sequence in context: A113119 A067416 A113671 * A034908 A030048 A054918
Adjacent sequences: A001759 A001760 A001761 * A001763 A001764 A001765
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from Wolfdieter Lang
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STATUS
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approved
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