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%I #9 Aug 12 2015 16:12:41
%S 1,-4,2,-4,-21,-136,-996,-8152,-73811,-733244,-7938186,-93126716,
%T -1178054657,-15998857056,-232339375664,-3594982133808,
%U -59070662442383,-1027605845674036,-18873206761567638,-365015243426704372,-7416392564276075453,-157957992952546414328
%N Coefficients in an asymptotic expansion of A261239 in falling factorials.
%H Vaclav Kotesovec, <a href="/A261254/b261254.txt">Table of n, a(n) for n = 0..446</a>
%F a(n) ~ -4 * n! * (1 - 5/n + 5/n^2 - 30/n^4 - 286/n^5 - 2960/n^6 - 34890/n^7 - 459705/n^8 - 6678641/n^9 - 105999991/n^10).
%F For n>0, a(n) = Sum_{k=1..n} A261253(k) * Stirling1(n-1, k-1).
%e A261239(n)/(-3*n!) ~ 1 - 4/n + 2/(n*(n-1)) - 4/(n*(n-1)*(n-2)) - 21/(n*(n-1)*(n-2)*(n-3)) - 136/(n*(n-1)*(n-2)*(n-3)*(n-4)) - 996/(n*(n-1)*(n-2)*(n-3)*(n-4)*(n-5)) - ... [coefficients are A261254]
%e A261239(n)/(-3*n!) ~ 1 - 4/n + 2/n^2 - 2/n^3 - 31/n^4 - 288/n^5 - 2939/n^6 - ... [coefficients are A261253]
%t CoefficientList[Assuming[Element[x, Reals], Series[E^(4/x) * x^4 / ExpIntegralEi[1/x]^4, {x, 0, 25}]], x]
%Y Cf. A003319, A260503, A259472, A261214, A261239, A261253.
%K sign
%O 0,2
%A _Vaclav Kotesovec_, Aug 12 2015
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