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A260503 Coefficients in an asymptotic expansion of sequence A003319.

%I A260503 #24 Aug 12 2015 15:16:50
%S A260503 1,-2,-1,-5,-32,-253,-2381,-25912,-319339,-4388949,-66495386,
%T A260503 -1100521327,-19751191053,-382062458174,-7924762051957,
%U A260503 -175478462117633,-4132047373455024,-103115456926017761,-2718766185148876961,-75529218928863243200,-2205316818199975235447
%N A260503 Coefficients in an asymptotic expansion of sequence A003319.
%H A260503 Vaclav Kotesovec, <a href="/A260503/b260503.txt">Table of n, a(n) for n = 0..420</a>
%F A260503 a(k) ~ -k! / (2 * (log(2))^(k+1)).
%F A260503 For n>0, Sum_{k=1..n} a(k) * Stirling1(n-1, k-1) = A259472(n). - _Vaclav Kotesovec_, Aug 03 2015
%F A260503 For n>0, a(n) = Sum_{k=1..n} A259472(k) * Stirling2(n-1, k-1). - _Vaclav Kotesovec_, Aug 03 2015
%e A260503 A003319(n) / n! ~ 1 - 2/n - 1/n^2 - 5/n^3 - 32/n^4 - 253/n^5 - 2381/n^6 - ...
%t A260503 Flatten[{1, Table[Sum[Assuming[Element[x,Reals], SeriesCoefficient[E^(2/x)*x^2 / ExpIntegralEi[1/x]^2,{x,0,k}]] * StirlingS2[n-1,k-1], {k,1,n}], {n,1,20}]}] (* _Vaclav Kotesovec_, Aug 03 2015 *)
%Y A260503 Cf. A003319, A259472, A261214, A261239, A261253, A261254.
%Y A260503 Cf. A256168, A260491, A260530, A260532, A260578.
%K A260503 sign
%O A260503 0,2
%A A260503 _Vaclav Kotesovec_, Jul 27 2015