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%I #11 Aug 05 2015 04:09:32
%S 1,2,5,17,74,395,2526,19087,168603,1723065,20148031,266437102,
%T 3938754720,64391209604,1152961464743,22424127879610,470399253269776,
%U 10579865622308851,253840801521314095,6468953273455413674,174452533187403980841,4962228907578051232358
%N Coefficients in asymptotic expansion of sequence A259870.
%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) ~ 2 * exp(-1) * (k-1)! / (log(2))^k.
%e A259870(n)/((n-1)!/exp(1)) ~ 1 + 2/n + 5/n^2 + 17/n^3 + 74/n^4 + 395/n^5 + ...
%t nmax = 25; b = CoefficientList[Assuming[Element[x, Reals], Series[x/(ExpIntegralEi[1 + 1/x]/Exp[1 + 1/x] - 1)^2, {x, 0, nmax+1}]], x]; Table[Sum[b[[k+1]]*StirlingS2[n, k-1], {k, 1, n+1}], {n, 0, nmax}]
%Y Cf. A259870, A260578, A260949, A260950.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Aug 05 2015