OFFSET
0,3
COMMENTS
For k > 1 is a(k) negative.
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.
FORMULA
a(k) ~ -k! / (2 * exp(1) * (log(2))^(k+1)).
EXAMPLE
A259869(n) / (n!/exp(1)) ~ 1 - 2/n^2 - 6/n^3 - 29/n^4 - 196/n^5 - 1665/n^6 - ...
MATHEMATICA
nmax = 20; b = CoefficientList[Assuming[Element[x, Reals], Series[x^2*E^(2 + 2/x)/ExpIntegralEi[1 + 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
KEYWORD
sign
AUTHOR
Vaclav Kotesovec, Jul 29 2015
STATUS
approved