OFFSET
1,2
LINKS
FORMULA
Divides by n and shifts left under "DIJ" (bracelet, indistinct, labeled) transform.
E.g.f: series reversion of 2*x/(2 + x + x^2/2 - log(1-x)). - Andrew Howroyd, Sep 19 2018
a(n) ~ sqrt(s) * (2 - s^2)^(n + 1/2) * n^n / (sqrt(2 - 2*s + s^2) * n * 2^n * (1-s)^(n - 1/2) * exp(n)), where s = 0.7579492001963653206343844374776312472163... is the root of the equation 4 - 6*s - s^2 + s^3 - 2*(1-s)*log(1-s) = 0. - Vaclav Kotesovec, Apr 21 2020
MATHEMATICA
m = 20;
CoefficientList[InverseSeries[2*x/(2 + x + x^2/2 - Log[1 - x]) + O[x]^m], x]*Range[0, m - 1]! // Rest (* Jean-François Alcover, Sep 08 2019 *)
PROG
(PARI) Vec(serlaplace(serreverse(2*x/(2 + x + x^2/2 - log(1-x + O(x^20)))))) \\ Andrew Howroyd, Sep 19 2018
CROSSREFS
KEYWORD
nonn,eigen
AUTHOR
EXTENSIONS
Terms a(17) and beyond from Andrew Howroyd, Sep 19 2018
STATUS
approved