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A277467
E.g.f.: tan(x)/(1+LambertW(-x)).
4
0, 1, 2, 14, 116, 1376, 19926, 346128, 6964712, 159396352, 4085415850, 115906440704, 3605365584732, 121998144397312, 4461190462108030, 175305587376883712, 7366747721719011280, 329646098258032459776, 15649117182518598570834, 785528920149992297070592
OFFSET
0,3
LINKS
FORMULA
a(n) ~ tan(exp(-1)) * n^n.
MATHEMATICA
CoefficientList[Series[Tan[x]/(1+LambertW[-x]), {x, 0, 25}], x] * Range[0, 25]!
Table[Sin[Pi*n/2] * 2^(n+1) * (2^(n+1) - 1) * BernoulliB[n+1] / (n+1) + Sum[Binomial[n, k] * Sin[Pi*k/2] * 2^(k+1) * (2^(k+1)-1) * BernoulliB[k+1] /(k+1) * (n-k)^(n-k), {k, 0, n-1}], {n, 0, 25}] (* Vaclav Kotesovec, Oct 28 2016 *)
PROG
(PARI) x='x+O('x^30); concat([0], Vec(serlaplace(tan(x)/(1 + lambertw(-x))))) \\ G. C. Greubel, May 29 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Oct 16 2016
STATUS
approved