A260491 Coefficients in asymptotic expansion of sequence A077607.

1, -4, 0, -8, -76, -752, -8460, -107520, -1522124, -23717424, -402941324, -7407988448, -146479479308, -3099229422352, -69863683041868, -1671667534710720, -42318672085310540, -1130167625049525232, -31758424368739424780, -936840101208573355680

Offset: 0

Author

Vaclav Kotesovec, Jul 27 2015

Keywords

• sign

Comments

For k > 2 is a(k) negative.

Examples

			A077607(n) / (-n!) ~ 1 - 4/n - 8/n^3 - 76/n^4 - 752/n^5 - 8460/n^6 - ...
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..126
• Richard J. Martin, and Michael J. Kearney, Integral representation of certain combinatorial recurrences, Combinatorica: 35:3 (2015), 309-315.

Crossrefs

Cf. A077607, A111529, A256168, A260503, A260530, A260532, A260578.

Programs

Mathematica

nmax = 30; b = CoefficientList[Assuming[Element[x, Reals], Series[x^4*E^(2/x)/(ExpIntegralEi[1/x] - x*E^(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 * k! / (4 * (log(2))^(k+2)).