A277468
E.g.f.: tanh(x)/(1+LambertW(-x)).
Original entry on oeis.org
0, 1, 2, 10, 100, 1216, 17766, 309744, 6260360, 143641600, 3688352650, 104786813440, 3263080663404, 110514370068480, 4044232154193518, 159019302501971968, 6685886706336107536, 299315231931854749696, 14214873507079452102162, 713784039156929684963328
Offset: 0
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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 *)
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x='x+O('x^50); concat([0], Vec(serlaplace(tanh(x)/(1 + lambertw(-x))))) \\ G. C. Greubel, Nov 05 2017
A277479
E.g.f.: -tan(x)*LambertW(-x).
Original entry on oeis.org
0, 0, 2, 6, 44, 360, 4206, 59584, 1021432, 20329344, 461596090, 11756157952, 331835099364, 10278341179392, 346555737301606, 12633922368061440, 495139124241620080, 20758413862397509632, 926980786260912379122, 43925328338613823078400, 2201264843743619567644700
Offset: 0
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CoefficientList[Series[-Tan[x]*LambertW[-x], {x, 0, 20}], x] * Range[0, 20]!
Table[Sum[Binomial[n, k] * Sin[Pi*k/2] * 2^(k+1) * (2^(k+1)-1) * BernoulliB[k+1] /(k+1) * (n-k)^(n-k-1), {k, 0, n-1}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 28 2016 *)
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x='x+O('x^50); concat([0,0], Vec(serlaplace(- tan(x)*lambertw(-x) ))) \\ G. C. Greubel, Nov 08 2017
A277500
E.g.f.: -LambertW(-tan(x)).
Original entry on oeis.org
0, 1, 2, 11, 80, 821, 10608, 167215, 3105024, 66433129, 1609025024, 43521156755, 1300287942656, 42528924900125, 1511407185512448, 57992816331075511, 2389444376908726272, 105219795048784564945, 4931495123285481881600, 245105773365008603770907
Offset: 0
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S:= series(-LambertW(-tan(x)),x,31):
seq(coeff(S,x,n)*n!,n=0..30); # Robert Israel, Mar 09 2017
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CoefficientList[Series[-LambertW[-Tan[x]], {x, 0, 20}], x] * Range[0, 20]!
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x='x+O('x^50); concat([0], Vec(serlaplace(-lambertw(-tan(x))))) \\ G. C. Greubel, Nov 07 2017
Showing 1-3 of 3 results.