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%I #15 Aug 12 2015 15:56:54
%S 1,-3,0,-4,-21,-129,-910,-7242,-64155,-626319,-6685548,-77527104,
%T -971315713,-13084909917,-188723009274,-2902997766470,-47458671376503,
%U -821951603042523,-15037432614035864,-289828080356525052,-5870642802374608509,-124691017072423632777
%N Coefficients in an asymptotic expansion of A259472 in falling factorials.
%H Vaclav Kotesovec, <a href="/A261239/b261239.txt">Table of n, a(n) for n = 0..446</a>
%F a(n) ~ -3 * n! * (1 - 4/n + 2/n^2 - 2/n^3 - 31/n^4 - 288/n^5 - 2939/n^6 - 33944/n^7 - 438614/n^8 - 6266312/n^9 - 98050303/n^10), coefficients are A261253.
%F For n>0, a(n) = Sum_{k=1..n} A261214(k) * Stirling1(n-1, k-1).
%e A259472(n)/(-2*n!) ~ 1 - 3/n - 4/(n*(n-1)*(n-2)) - 21/(n*(n-1)*(n-2)*(n-3)) - 129/(n*(n-1)*(n-2)*(n-3)*(n-4)) - ... [coefficients are A261239]
%e A259472(n)/(-2*n!) ~ 1 - 3/n - 4/n^3 - 33/n^4 - 283/n^5 - 2785/n^6 - ... [coefficients are A261214]
%t CoefficientList[Assuming[Element[x, Reals], Series[E^(3/x) * x^3 / ExpIntegralEi[1/x]^3, {x, 0, 25}]], x]
%Y Cf. A003319, A260503, A259472, A261214, A261253, A261254.
%K sign
%O 0,2
%A _Vaclav Kotesovec_, Aug 12 2015
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