OFFSET
0,2
COMMENTS
For k > 2 is a(k) negative.
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..126
Richard J. Martin, and Michael J. Kearney, Integral representation of certain combinatorial recurrences, Combinatorica: 35:3 (2015), 309-315.
FORMULA
a(k) ~ -k * k! / (4 * (log(2))^(k+2)).
EXAMPLE
A077607(n) / (-n!) ~ 1 - 4/n - 8/n^3 - 76/n^4 - 752/n^5 - 8460/n^6 - ...
MATHEMATICA
nmax = 30; b = CoefficientList[Assuming[Element[x, Reals], Series[x^4*E^(2/x)/(ExpIntegralEi[1/x] - 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
KEYWORD
sign
AUTHOR
Vaclav Kotesovec, Jul 27 2015
STATUS
approved