A261253 Coefficients in an asymptotic expansion of sequence A261239.

1, -4, 2, -2, -31, -288, -2939, -33944, -438614, -6266312, -98050303, -1667563622, -30631857759, -604518210964, -12758658946466, -286833669370926, -6844757550430019, -172833310268551740, -4604828067485736507, -129123684195177403168, -3801830662346341617586

Offset: 0

Author

Vaclav Kotesovec, Aug 12 2015

Keywords

• sign

Examples

			A261239(n)/(-3*n!) ~ 1 - 4/n + 2/n^2 - 2/n^3 - 31/n^4 - 288/n^5 - 2939/n^6 - ...
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..400

Crossrefs

Cf. A003319, A260503, A259472, A261214, A261239, A261254.

Programs

Mathematica

Flatten[{1, Table[Sum[CoefficientList[Assuming[Element[x, Reals], Series[E^(4/x)*x^4/ExpIntegralEi[1/x]^4, {x, 0, 25}]], x][[k+1]] * StirlingS2[n-1, k-1], {k, 1, n}], {n, 1, 25}]}]

Formula

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

For n>0, a(n) = Sum_{k=1..n} A261254(k) * Stirling2(n-1, k-1).