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%I #11 Aug 05 2015 04:10:25
%S 1,0,-2,-6,-29,-196,-1665,-16796,-194905,-2549468,-37055681,
%T -592013436,-10307671769,-194225544124,-3937581243201,-85460277981116,
%U -1977127315636969,-48573021658496348,-1262954975286604673,-34650561545808167292,-1000438355724912080873
%N Coefficients in asymptotic expansion of sequence A259869.
%C For k > 1 is a(k) negative.
%H Vaclav Kotesovec, <a href="/A260578/b260578.txt">Table of n, a(n) for n = 0..132</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! / (2 * exp(1) * (log(2))^(k+1)).
%e A259869(n) / (n!/exp(1)) ~ 1 - 2/n^2 - 6/n^3 - 29/n^4 - 196/n^5 - 1665/n^6 - ...
%t nmax = 20; b = CoefficientList[Assuming[Element[x, Reals], Series[x^2*E^(2 + 2/x)/ExpIntegralEi[1 + 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. A259869, A256168, A260491, A260503, A260530, A260532, A260948, A260949, A260950.
%K sign
%O 0,3
%A _Vaclav Kotesovec_, Jul 29 2015
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