A277483 -id:A277483 - cp's OEIS frontend

A277502 E.g.f.: -LambertW(-arcsin(x)).

0, 1, 2, 10, 72, 724, 9184, 142080, 2587392, 54290256, 1289277440, 34191270752, 1001513996288, 32113767783616, 1118831623585792, 42084750888906240, 1699836383279448064, 73377208318764134656, 3371248736937012363264, 164251735270613613412864

Offset: 0

Vaclav Kotesovec, Oct 18 2016

nonn

G. C. Greubel, Table of n, a(n) for n = 0..385

Cf. A277469, A277483, A277503.

CoefficientList[Series[-LambertW[-ArcSin[x]], {x, 0, 20}], x] * Range[0, 20]!

x='x+O('x^30); concat([0], Vec(serlaplace(-lambertw(-asin(x))))) \\ G. C. Greubel, Nov 12 2017

a(n) ~ sqrt(tan(exp(-1))) * exp(1/2 - n) * n^(n-1) / sin(exp(-1))^n.

A277484 E.g.f.: -arcsinh(x)*LambertW(-x).

Original entry on oeis.org

0, 0, 2, 6, 32, 300, 3624, 52570, 908928, 18277560, 417634080, 10682763278, 302517156864, 9394763009060, 317429118686848, 11592017133950370, 454961391572119552, 19097430979664893168, 853711115246721262080, 40490675416206345889686, 2030782746261324446228480

Offset: 0

Vaclav Kotesovec, Oct 17 2016

nonn

G. C. Greubel, Table of n, a(n) for n = 0..385

Cf. A000169, A277470, A277473, A277483.

CoefficientList[Series[-ArcSinh[x]*LambertW[-x], {x, 0, 20}], x] * Range[0, 20]!
Flatten[{0, Table[Sum[Sin[Pi*k/2] * Binomial[n, k] * (k-2)!!^2 * (n-k)^(n-k-1), {k, 1, n-1}], {n, 1, 20}]}] (* Vaclav Kotesovec, Oct 28 2016 *)

x='x+O('x^10); concat([0,0], Vec(serlaplace(-asinh(x)*lambertw(-x) ))) \\ G. C. Greubel, Nov 08 2017

a(n) ~ arcsinh(exp(-1)) * n^(n-1).

a(n) ~ (-1 + log(1 + sqrt(1+exp(2)))) * n^(n-1).

cp's OEIS Frontend

A277502 E.g.f.: -LambertW(-arcsin(x)).

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