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%I #30 May 25 2020 11:06:13
%S 1,0,2,0,8,16,96,464,2848,19056,142400,1166608,10411488,100496816,
%T 1043154304,11585854032,137089725728,1721562067696,22867314748608,
%U 320313336833936,4718773157942368,72932090897154096,1180003546791130112,19945632339806733520,351569488641977570208
%N Coefficients in asymptotic (divergent) expansion for Sum_{k=1..n} 1/C(n,k)^2.
%C A005649 gives asymptotic divergent expansion for Sum_{k=0..n} 1/C(n,k).
%H Vaclav Kotesovec, <a href="/A076687/b076687.txt">Table of n, a(n) for n = 0..100</a>
%F 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 + ...
%F a(m) ~ Pi * m^(m+1) / (2^(m+3) * (log(2))^(m + 3/2) * exp(m)). - _Vaclav Kotesovec_, May 25 2020
%e Sum_{k=1..1000} 1/C(1000,k)^2 = 1.000002000008016096466....
%t 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 *)
%Y Cf. A005649.
%K nonn
%O 0,3
%A _Benoit Cloitre_, Oct 25 2002
%E Corrected and extended by _Vladeta Jovovic_, Oct 26 2007
%E Corrected by _Vaclav Kotesovec_, May 25 2020
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