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Search: id:A079678
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| A079678 |
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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=5. |
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+0
1
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| 1, 10, 115, 1360, 16265, 195660, 2361925, 28577440, 346316645, 4201744870, 51023399190, 620022989200, 7538489480075, 91696845873760, 1115794688036920, 13581508654978560, 165357977228808925, 2013721466517360650
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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)=5/8*(3125/256)^n*(1+c/sqrt(n)+o(n^-1/2)) where c=0.356...
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CROSSREFS
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Sequence in context: A024130 A104520 A138845 this_sequence A089833 A083448 A024129
Adjacent sequences: A079675 A079676 A079677 this_sequence A079679 A079680 A079681
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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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