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A260530 Coefficients in asymptotic expansion of sequence A051296.

%I A260530 #14 Aug 05 2015 04:05:59
%S A260530 1,2,7,35,216,1575,13243,126508,1359437,16312915,217277446,3194459333,
%T A260530 51557948291,908431129702,17376289236947,358847480175063,
%U A260530 7959468559605624,188702262366570387,4760773506835189975,127312428854513811012,3596091234340397964321
%N A260530 Coefficients in asymptotic expansion of sequence A051296.
%H A260530 Vaclav Kotesovec, <a href="/A260530/b260530.txt">Table of n, a(n) for n = 0..132</a>
%H A260530 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 A260530 a(k) ~ k! / (2 * (log(2))^(k+1)).
%e A260530 A051296(n) / n! ~ 1 + 2/n + 7/n^2 + 35/n^3 + 216/n^4 + 1575/n^5 + 13243/n^6 + ...
%t A260530 nmax = 30; b = CoefficientList[Assuming[Element[x, Reals], Series[E^(2/x)*x^2 / (ExpIntegralEi[1/x] - 2*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 A260530 Cf. A051296, A256168, A260491, A260503, A260532, A260578.
%K A260530 nonn
%O A260530 0,2
%A A260530 _Vaclav Kotesovec_, Jul 28 2015