A256168 Coefficients in asymptotic expansion of sequence A052186.

1, -2, 1, -1, -9, -59, -474, -4560, -50364, -625385, -8622658, -130751886, -2163331779, -38793751015, -749691306018, -15535914341831, -343749787006758, -8089725377931547, -201801866906374263, -5319643146604299835, -147774950436327236681

Offset

0,2

Comments

For k > 2 is a(k) negative.

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..394

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

Formula

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

Example

A052186(n) / n! ~ 1 - 2/n + 1/n^2 - 1/n^3 - 9/n^4 - 59/n^5 - 474/n^6 - ...

Mathematica

nmax = 30; b = CoefficientList[Assuming[Element[x, Reals], Series[E^(2/x) / (ExpIntegralEi[1/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 *)

Crossrefs

Cf. A052186, A260491, A260503, A260530, A260532, A260578.

Sequence in context: A283321 A155718 A327088 * A054768 A104251 A320576

Adjacent sequences: A256165 A256166 A256167 * A256169 A256170 A256171

Keyword

sign

Author

Vaclav Kotesovec, Mar 17 2015

Status

approved