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

0,2

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.

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

Example

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

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 *)

Crossrefs

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

Sequence in context: A227119 A002872 A105216 * A193657 A007164 A321208

Adjacent sequences: A260529 A260530 A260531 * A260533 A260534 A260535

Keyword

nonn

Author

Vaclav Kotesovec, Jul 28 2015

Status

approved