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Search: id:A079563
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| A079563 |
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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=7. |
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+0
1
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| 1, 14, 231, 3934, 67851, 1177974, 20531770, 358788696, 6281076123, 110103674128, 1931983053056, 33926800240578, 596145343139514, 10480467311987778, 184327560283768776, 3243034966775972144, 57074433199551436347
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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)=(7/12)*(823543/46656)^n*(1+c/sqrt(n)+o(n^-1/2)) where c=0.41...
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CROSSREFS
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Sequence in context: A027774 A099272 A120048 this_sequence A166774 A055477 A123774
Adjacent sequences: A079560 A079561 A079562 this_sequence A079564 A079565 A079566
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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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