A260578 Coefficients in asymptotic expansion of sequence A259869.

1, 0, -2, -6, -29, -196, -1665, -16796, -194905, -2549468, -37055681, -592013436, -10307671769, -194225544124, -3937581243201, -85460277981116, -1977127315636969, -48573021658496348, -1262954975286604673, -34650561545808167292, -1000438355724912080873

Offset: 0

Author

Vaclav Kotesovec, Jul 29 2015

Keywords

• sign

Comments

For k > 1 is a(k) negative.

Examples

			A259869(n) / (n!/exp(1)) ~ 1 - 2/n^2 - 6/n^3 - 29/n^4 - 196/n^5 - 1665/n^6 - ...
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..132
• Richard J. Martin, and Michael J. Kearney, Integral representation of certain combinatorial recurrences, Combinatorica: 35:3 (2015), 309-315.

Crossrefs

Cf. A259869, A256168, A260491, A260503, A260530, A260532, A260948, A260949, A260950.

Programs

Mathematica

nmax = 20; b = CoefficientList[Assuming[Element[x, Reals], Series[x^2*E^(2 + 2/x)/ExpIntegralEi[1 + 1/x]^2, {x, 0, nmax}]], x]; Flatten[{1, Table[Sum[b[[k+1]]*StirlingS2[n-1, k-1], {k, 1, n}], {n, 1, nmax}]}] (* Vaclav Kotesovec, Aug 03 2015 *)

Formula

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