Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #10 Aug 12 2015 16:12:31
%S 1,-4,2,-2,-31,-288,-2939,-33944,-438614,-6266312,-98050303,
%T -1667563622,-30631857759,-604518210964,-12758658946466,
%U -286833669370926,-6844757550430019,-172833310268551740,-4604828067485736507,-129123684195177403168,-3801830662346341617586
%N Coefficients in an asymptotic expansion of sequence A261239.
%H Vaclav Kotesovec, <a href="/A261253/b261253.txt">Table of n, a(n) for n = 0..400</a>
%F a(k) ~ -k! / (log(2))^(k+1).
%F For n>0, a(n) = Sum_{k=1..n} A261254(k) * Stirling2(n-1, k-1).
%e A261239(n)/(-3*n!) ~ 1 - 4/n + 2/n^2 - 2/n^3 - 31/n^4 - 288/n^5 - 2939/n^6 - ...
%t Flatten[{1, Table[Sum[CoefficientList[Assuming[Element[x, Reals], Series[E^(4/x)*x^4/ExpIntegralEi[1/x]^4, {x, 0, 25}]], x][[k+1]] * StirlingS2[n-1, k-1], {k, 1, n}], {n, 1, 25}]}]
%Y Cf. A003319, A260503, A259472, A261214, A261239, A261254.
%K sign
%O 0,2
%A _Vaclav Kotesovec_, Aug 12 2015