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A260491 Coefficients in asymptotic expansion of sequence A077607.

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%I A260491 #20 Aug 05 2015 04:06:59
%S A260491 1,-4,0,-8,-76,-752,-8460,-107520,-1522124,-23717424,-402941324,
%T A260491 -7407988448,-146479479308,-3099229422352,-69863683041868,
%U A260491 -1671667534710720,-42318672085310540,-1130167625049525232,-31758424368739424780,-936840101208573355680
%N A260491 Coefficients in asymptotic expansion of sequence A077607.
%C A260491 For k > 2 is a(k) negative.
%H A260491 Vaclav Kotesovec, <a href="/A260491/b260491.txt">Table of n, a(n) for n = 0..126</a>
%H A260491 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 A260491 a(k) ~ -k * k! / (4 * (log(2))^(k+2)).
%e A260491 A077607(n) / (-n!) ~ 1 - 4/n - 8/n^3 - 76/n^4 - 752/n^5 - 8460/n^6 - ...
%t A260491 nmax = 30; b = CoefficientList[Assuming[Element[x, Reals], Series[x^4*E^(2/x)/(ExpIntegralEi[1/x] - 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 A260491 Cf. A077607, A111529, A256168, A260503, A260530, A260532, A260578.
%K A260491 sign
%O A260491 0,2
%A A260491 _Vaclav Kotesovec_, Jul 27 2015