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Search: id:A006256
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| A006256 |
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Sum C(3k,k)*C(3n-3k,n-k), k = 0 . . n.
(Formerly M4229)
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+0
7
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| 1, 6, 39, 258, 1719, 11496, 77052, 517194, 3475071, 23366598, 157206519, 1058119992, 7124428836, 47983020624, 323240752272, 2177956129818, 14677216121871, 98923498131762, 666819212874501, 4495342330033938, 30308036621747679
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Convolution of A005809 with itself. - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 22 2003
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
D. Merlini, R. Sprugnoli and M. C. Verri, The tennis ball problem, J. Combin. Theory, A 99 (2002), 307-344 (Y_n for s=3).
M. Petkovsek et al., A=B, Peters, 1996, p. 165.
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FORMULA
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a(n)=3/4*(27/4)^n*(1+c/sqrt(n)+o(n^(-1/2))) where c=0.21713... 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, A078995 for cases m=2 and 4. - Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 26 2003
G.f.: 1/(1-3zg^2)^2, where g=g(z) is given by g=1+zg^3, g(0)=1, i.e. (in Maple command) g := 2*sin(arcsin(3*sqrt(3*z)/2)/3)/sqrt(3*z); - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 22 2003
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CROSSREFS
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Cf. A036829.
Sequence in context: A037683 A145664 A090018 this_sequence A052392 A147961 A068765
Adjacent sequences: A006253 A006254 A006255 this_sequence A006257 A006258 A006259
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), D. E. Knuth
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