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Search: id:A078995
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| A078995 |
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Sum_{k=0..n} C(4*k,k)*C(4*(n-k),n-k). |
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+0
6
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| 1, 8, 72, 664, 6184, 57888, 543544, 5113872, 48180456, 454396000, 4288773152, 40503496536, 382701222296, 3617396099936, 34203591636048, 323492394385824, 3060238763412072, 28955508198895584, 274018698082833760, 2593539713410178528, 24550565251665845664
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OFFSET
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0,2
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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 (Y_n for s=4).
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FORMULA
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a(n)=4/3*(256/27)^n*(1+c/sqrt(n)+o(n^-1/2)) where c=0.307... 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 for cases m=2 and 3. - Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 26 2003
243*n*(8*n - 17)*(3*n - 1)*(3*n - 4)*(3*n - 2)*(3*n - 5)*a(n) = 72*(3*n - 5)*(3*n - 4)*(6912*n^4 - 33120*n^3 + 58256*n^2 - 47798*n + 15309)*a(n - 1) - 3072*(2*n - 3)*(6912*n^5 - 55008*n^4 + 175696*n^3 - 282180*n^2 + 227825*n - 73710)*a(n - 2) + 262144*(n - 2)*(4*n - 7)*(2*n - 3)*(2*n - 5)*(4*n - 9)*(8*n - 9)*a(n - 3). - Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 16 2004
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CROSSREFS
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See A049235 for more information.
Sequence in context: A155198 A147840 A115970 this_sequence A082414 A145303 A098411
Adjacent sequences: A078992 A078993 A078994 this_sequence A078996 A078997 A078998
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Jan 19 2003
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