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Search: id:A079679
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| A079679 |
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a(n)=a(n,m)=sum(k=0,n,binomial(m*k,k)*binomial(m*(n-k),n-k)) for m=6. |
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+0
1
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| 1, 12, 168, 2424, 35400, 520236, 7674144, 113482584, 1681028136, 24932533800, 370144424376, 5499182587416, 81748907485248, 1215834858032820, 18090048027643200, 269246037610828656, 4008495234662771688
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OFFSET
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0,2
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COMMENT
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more generally : a(n,m)=sum(k=0,n,binomial(m*k,k)*binomial(m*(n-k),n-k)) is asymptotic to 1/2*m/(m-1)*(m^m/(m-1)^(m-1))^n. See A000302, A006256, A078995 for cases m=2,3 and 4.
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REFERENCES
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D. Merlini, R. Sprugnoli and M. C. Verri, The tennis ball problem, J.Combin. Theory, A 99 (2002), 307-344
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FORMULA
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a(n)=3/5*(46656/3125)^n*(1+c/sqrt(n)+o(n^-1/2)) where c=0.388...
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CROSSREFS
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Adjacent sequences: A079676 A079677 A079678 this_sequence A079680 A079681 A079682
Sequence in context: A055760 A056591 A099745 this_sequence A113380 A071103 A012489
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 26 2003
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