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A277468
E.g.f.: tanh(x)/(1+LambertW(-x)).
5
0, 1, 2, 10, 100, 1216, 17766, 309744, 6260360, 143641600, 3688352650, 104786813440, 3263080663404, 110514370068480, 4044232154193518, 159019302501971968, 6685886706336107536, 299315231931854749696, 14214873507079452102162, 713784039156929684963328
OFFSET
0,3
LINKS
FORMULA
a(n) ~ tanh(exp(-1)) * n^n.
MATHEMATICA
CoefficientList[Series[Tanh[x]/(1+LambertW[-x]), {x, 0, 25}], x] * Range[0, 25]!
Flatten[{0, Table[2^(n+1)*(2^(n+1) - 1)*BernoulliB[n+1]/(n+1) + Sum[Binomial[n, k]*2^(k+1)*(2^(k+1) - 1) * BernoulliB[k+1]/(k+1)*(n-k)^(n-k), {k, 1, n-1}], {n, 1, 25}]}] (* Vaclav Kotesovec, Oct 28 2016 *)
PROG
(PARI) x='x+O('x^50); concat([0], Vec(serlaplace(tanh(x)/(1 + lambertw(-x))))) \\ G. C. Greubel, Nov 05 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Oct 16 2016
STATUS
approved