A260532 Coefficients in asymptotic expansion of sequence A051295.

1, 2, 7, 31, 165, 1025, 7310, 59284, 543702, 5618267, 65200918, 846462826, 12229783811, 195394019337, 3427472046792, 65526442181293, 1355785469986828, 30166624979467869, 717769036033944699, 18174105506247664633, 487655384740384445407, 13816406622559942660420

Offset: 0

Author

Vaclav Kotesovec, Jul 28 2015

Keywords

• nonn

Examples

			A051295(n)/(n-1)! ~ 1 + 2/n + 7/n^2 + 31/n^3 + 165/n^4 + 1025/n^5 + 7310/n^6 + ...
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..134
• Richard J. Martin, and Michael J. Kearney, Integral representation of certain combinatorial recurrences, Combinatorica: 35:3 (2015), 309-315.

Crossrefs

Cf. A051295, A134378, A256168, A260491, A260503, A260530, A260578.

Programs

Mathematica

nmax = 30; b = CoefficientList[Assuming[Element[x, Reals], Series[E^(2/x)*x / (ExpIntegralEi[1/x] - E^(1/x))^2, {x, 0, nmax+1}]], x]; Table[Sum[b[[k+1]] * StirlingS2[n, k-1], {k, 1, n+1}], {n, 0, nmax}] (* Vaclav Kotesovec, Aug 03 2015 *)

Formula

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

a(n) = Sum_{k=0..n} A134378(k) * Stirling2(n, k). - Vaclav Kotesovec, Aug 04 2015