A261214 Coefficients in an asymptotic expansion of sequence A259472.

1, -3, 0, -4, -33, -283, -2785, -31291, -395360, -5544754, -85427259, -1433955817, -26046643595, -509070113635, -10653941722236, -237754202827284, -5636787946661521, -141514316248243499, -3751121064314067653, -104704135027419849139, -3070176356776990397500

Offset: 0

Author

Vaclav Kotesovec, Aug 12 2015

Keywords

• sign

Examples

			A259472(n)/(-2*n!) ~ 1 - 3/n - 4/n^3 - 33/n^4 - 283/n^5 - 2785/n^6 - ...
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..110

Crossrefs

Cf. A003319, A260503, A259472, A261239, A261253, A261254.

Programs

Mathematica

Flatten[{1, Table[Sum[CoefficientList[Assuming[Element[x, Reals], Series[E^(3/x)*x^3/ExpIntegralEi[1/x]^3, {x, 0, 25}]], x][[k+1]] * StirlingS2[n-1, k-1], {k, 1, n}], {n, 1, 20}]}]

Formula

a(k) ~ -3 * k! / (4 * (log(2))^(k+1)).

For n>0, a(n) = Sum_{k=1..n} A261239(k) * Stirling2(n-1, k-1).