|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
STATUS
|
approved
|
|
|
|