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Search: id:A018901
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| A018901 |
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Central hexanomial coefficients: largest coefficient of (1+x+...+x^5)^n. |
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+0
12
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| 1, 1, 6, 27, 146, 780, 4332, 24017, 135954, 767394, 4395456, 25090131, 144840476, 833196442, 4836766584, 27981391815, 163112472594, 947712321234, 5542414273884, 32312202610863, 189456975899496, 1107575676600876
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Greatest multiplicity of one- or two-dimensional standard representation of Lie algebras sl(2) in decomposition of tensor power F6^k, where F6 is the standard 6-dimensional irreducible representation of sl(2). - Leonid Bedratiuk (bedratyuk(AT)ief.tup.km.ua), Jul 22 2004
Sum((-1)^(k)*binomial(n,k)*binomial(n+floor(5*n/2)-6*k-1, n-1), k=0..floor(5*n/12)). - Warut Roonguthai (warut822(AT)yahoo.com), May 21 2006
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..200
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EXAMPLE
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Number of ways of getting most likely sum using n 6-sided dice (e.g. for n=2, 7 is the most prevalent sum and there are 6 different ways to get it: 1-6, 2-5, 3-4, 4-3, 5-2, 6-1).
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MAPLE
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sum((-1)^(k)*binomial(n, k)*binomial(n+floor(5*n/2)-6*k-1, n-1), k=0..floor(5*n/12)); - Warut Roonguthai (warut822(AT)yahoo.com), May 21 2006
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CROSSREFS
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Cf. A001405, A002426, A005190, A005191, A025012, A025013, A025014
Sequence in context: A109115 A038176 A104745 this_sequence A137968 A087297 A117336
Adjacent sequences: A018898 A018899 A018900 this_sequence A018902 A018903 A018904
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KEYWORD
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nonn
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AUTHOR
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Jonn Dalton jdalton(AT)vnet.ibm.com
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