A277470
E.g.f.: arcsinh(x)/(1+LambertW(-x)).
Original entry on oeis.org
0, 1, 2, 11, 104, 1249, 18264, 318163, 6425152, 147344769, 3781848480, 107408279483, 3343875651456, 113227469886881, 4142804357946240, 162871544915116035, 6847004160475236352, 306495323034774157569, 14554502490109085839872, 730777840212988501198059
Offset: 0
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CoefficientList[Series[ArcSinh[x]/(1+LambertW[-x]), {x, 0, 25}], x] * Range[0, 25]!
Flatten[{0, Table[Sin[Pi*n/2] * (n-2)!!^2 + Sum[Sin[Pi*k/2] * Binomial[n, k] * (k-2)!!^2 * (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(asinh(x)/(1 + lambertw(-x)) ))) \\ G. C. Greubel, Nov 07 2017
A277483
E.g.f.: -arcsin(x)*LambertW(-x).
Original entry on oeis.org
0, 0, 2, 6, 40, 340, 3984, 57050, 982528, 19616328, 446355840, 11384327438, 321701896704, 9973046260060, 336499112011776, 12274383608508450, 481282311712489472, 20185816487436968208, 901732370496365076480, 42742176871086712813974, 2142556308913381810012160
Offset: 0
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CoefficientList[Series[-ArcSin[x]*LambertW[-x], {x, 0, 20}], x] * Range[0, 20]!
Flatten[{0, Table[Sum[Binomial[n, k] * (1-(-1)^k)/2 * (k-2)!!^2 * (n-k)^(n-k-1), {k, 1, n-1}], {n, 1, 20}]}] (* Vaclav Kotesovec, Oct 28 2016 *)
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x='x+O('x^50); concat([0,0], Vec(serlaplace(- asin(x)*lambertw(-x) ))) \\ G. C. Greubel, Nov 08 2017
A277502
E.g.f.: -LambertW(-arcsin(x)).
Original entry on oeis.org
0, 1, 2, 10, 72, 724, 9184, 142080, 2587392, 54290256, 1289277440, 34191270752, 1001513996288, 32113767783616, 1118831623585792, 42084750888906240, 1699836383279448064, 73377208318764134656, 3371248736937012363264, 164251735270613613412864
Offset: 0
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CoefficientList[Series[-LambertW[-ArcSin[x]], {x, 0, 20}], x] * Range[0, 20]!
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x='x+O('x^30); concat([0], Vec(serlaplace(-lambertw(-asin(x))))) \\ G. C. Greubel, Nov 12 2017
Showing 1-3 of 3 results.