A260950 Coefficients in asymptotic expansion of sequence A259872.

1, -2, 1, 1, -10, -61, -382, -3489, -39001, -484075, -6619449, -99610098, -1638687448, -29255834780, -563343011377, -11639759292186, -256916737692132, -6034068201092777, -150271333127027481, -3955735249215111270, -109757859467421502791

Offset: 0

Author

Vaclav Kotesovec, Aug 05 2015

Keywords

• sign

Examples

			A259872(n)/((n-1)!/exp(1)) ~ 1 - 2/n + 1/n^2 + 1/n^3 - 10/n^4 - 61/n^5 - ...
		

Links

• Richard J. Martin, and Michael J. Kearney, Integral representation of certain combinatorial recurrences, Combinatorica: 35:3 (2015), 309-315.

Crossrefs

Cf. A259872, A260578, A260948, A260949.

Programs

Mathematica

nmax = 25; b = CoefficientList[Assuming[Element[x, Reals], Series[x/(ExpIntegralEi[1 + 1/x]/Exp[1 + 1/x] + 1)^2, {x, 0, nmax+1}]], x]; Table[Sum[b[[k+1]]*StirlingS2[n, k-1], {k, 1, n+1}], {n, 0, nmax}]

Formula

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