A260530 Coefficients in asymptotic expansion of sequence A051296.

1, 2, 7, 35, 216, 1575, 13243, 126508, 1359437, 16312915, 217277446, 3194459333, 51557948291, 908431129702, 17376289236947, 358847480175063, 7959468559605624, 188702262366570387, 4760773506835189975, 127312428854513811012, 3596091234340397964321

Offset: 0

Author

Vaclav Kotesovec, Jul 28 2015

Keywords

• nonn

Examples

			A051296(n) / n! ~ 1 + 2/n + 7/n^2 + 35/n^3 + 216/n^4 + 1575/n^5 + 13243/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. A051296, A256168, A260491, A260503, A260532, A260578.

Programs

Mathematica

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