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Coefficients in an asymptotic expansion of sequence A259472.
7

%I #14 Aug 12 2015 15:57:17

%S 1,-3,0,-4,-33,-283,-2785,-31291,-395360,-5544754,-85427259,

%T -1433955817,-26046643595,-509070113635,-10653941722236,

%U -237754202827284,-5636787946661521,-141514316248243499,-3751121064314067653,-104704135027419849139,-3070176356776990397500

%N Coefficients in an asymptotic expansion of sequence A259472.

%H Vaclav Kotesovec, <a href="/A261214/b261214.txt">Table of n, a(n) for n = 0..110</a>

%F a(k) ~ -3 * k! / (4 * (log(2))^(k+1)).

%F For n>0, a(n) = Sum_{k=1..n} A261239(k) * Stirling2(n-1, k-1).

%e A259472(n)/(-2*n!) ~ 1 - 3/n - 4/n^3 - 33/n^4 - 283/n^5 - 2785/n^6 - ...

%t Flatten[{1, Table[Sum[CoefficientList[Assuming[Element[x, Reals], Series[E^(3/x)*x^3/ExpIntegralEi[1/x]^3, {x, 0, 25}]], x][[k+1]] * StirlingS2[n-1, k-1], {k, 1, n}], {n, 1, 20}]}]

%Y Cf. A003319, A260503, A259472, A261239, A261253, A261254.

%K sign

%O 0,2

%A _Vaclav Kotesovec_, Aug 12 2015