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A260578
Coefficients in asymptotic expansion of sequence A259869.
11
1, 0, -2, -6, -29, -196, -1665, -16796, -194905, -2549468, -37055681, -592013436, -10307671769, -194225544124, -3937581243201, -85460277981116, -1977127315636969, -48573021658496348, -1262954975286604673, -34650561545808167292, -1000438355724912080873
OFFSET
0,3
COMMENTS
For k > 1 is a(k) negative.
LINKS
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 *)
KEYWORD
sign
AUTHOR
Vaclav Kotesovec, Jul 29 2015
STATUS
approved