A261254 Coefficients in an asymptotic expansion of A261239 in falling factorials.

1, -4, 2, -4, -21, -136, -996, -8152, -73811, -733244, -7938186, -93126716, -1178054657, -15998857056, -232339375664, -3594982133808, -59070662442383, -1027605845674036, -18873206761567638, -365015243426704372, -7416392564276075453, -157957992952546414328

Offset: 0

Author

Vaclav Kotesovec, Aug 12 2015

Keywords

• sign

Examples

			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]
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]
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..446

Crossrefs

Cf. A003319, A260503, A259472, A261214, A261239, A261253.

Programs

Mathematica

CoefficientList[Assuming[Element[x, Reals], Series[E^(4/x) * x^4 / ExpIntegralEi[1/x]^4, {x, 0, 25}]], x]

Formula

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).

For n>0, a(n) = Sum_{k=1..n} A261253(k) * Stirling1(n-1, k-1).