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A076687
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Coefficients in asymptotic (divergent) expansion for Sum_{k=1..n} 1/C(n,k)^2.
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1
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1, 0, 2, 0, 8, 16, 96, 464, 2848, 19056, 142400, 1166608, 10411488, 100496816, 1043154304, 11585854032, 137089725728, 1721562067696, 22867314748608, 320313336833936, 4718773157942368, 72932090897154096, 1180003546791130112, 19945632339806733520, 351569488641977570208
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OFFSET
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0,3
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COMMENTS
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A005649 gives asymptotic divergent expansion for Sum_{k=0..n} 1/C(n,k).
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LINKS
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FORMULA
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Sum_{k>=1} 1/C(n, k)^2 = 1/n^0 + 0/n^1 + 2/n^2 + 0/n^3 + 8/n^4 + 16/n^5 + 96/n^6 + ...
a(m) ~ Pi * m^(m+1) / (2^(m+3) * (log(2))^(m + 3/2) * exp(m)). - Vaclav Kotesovec, May 25 2020
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EXAMPLE
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Sum_{k=1..1000} 1/C(1000,k)^2 = 1.000002000008016096466....
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MATHEMATICA
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nmax = 30; CoefficientList[1 + 2*Total[Table[Normal[Series[1/Binomial[n, k]^2, {n, Infinity, nmax}]], {k, 1, nmax/2}]], 1/n] (* Vaclav Kotesovec, May 25 2020 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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