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%I #17 Aug 05 2015 04:06:27
%S 1,-2,1,-1,-9,-59,-474,-4560,-50364,-625385,-8622658,-130751886,
%T -2163331779,-38793751015,-749691306018,-15535914341831,
%U -343749787006758,-8089725377931547,-201801866906374263,-5319643146604299835,-147774950436327236681
%N Coefficients in asymptotic expansion of sequence A052186.
%C For k > 2 is a(k) negative.
%H Vaclav Kotesovec, <a href="/A256168/b256168.txt">Table of n, a(n) for n = 0..394</a>
%H Richard J. Martin, and Michael J. Kearney, <a href="http://dx.doi.org/10.1007/s00493-014-3183-3">Integral representation of certain combinatorial recurrences</a>, Combinatorica: 35:3 (2015), 309-315.
%F a(k) ~ -(k-1)! / (log(2))^k.
%e A052186(n) / n! ~ 1 - 2/n + 1/n^2 - 1/n^3 - 9/n^4 - 59/n^5 - 474/n^6 - ...
%t nmax = 30; b = CoefficientList[Assuming[Element[x, Reals], Series[E^(2/x) / (ExpIntegralEi[1/x] + E^(1/x))^2, {x, 0, nmax}]], x]; Flatten[{1, Table[Sum[b[[k+1]]*StirlingS2[n-1, k-1], {k, 1, n}], {n, 1, nmax}]}] (* _Vaclav Kotesovec_, Aug 03 2015 *)
%Y Cf. A052186, A260491, A260503, A260530, A260532, A260578.
%K sign
%O 0,2
%A _Vaclav Kotesovec_, Mar 17 2015