%I #10 Aug 05 2015 04:10:09

%S 1,-2,1,1,-10,-61,-382,-3489,-39001,-484075,-6619449,-99610098,

%T -1638687448,-29255834780,-563343011377,-11639759292186,

%U -256916737692132,-6034068201092777,-150271333127027481,-3955735249215111270,-109757859467421502791

%N Coefficients in asymptotic expansion of sequence A259872.

%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 A259872(n)/((n-1)!/exp(1)) ~ 1 - 2/n + 1/n^2 + 1/n^3 - 10/n^4 - 61/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. A259872, A260578, A260948, A260949.

%K sign

%O 0,2

%A _Vaclav Kotesovec_, Aug 05 2015