A277470 -id:A277470 - cp's OEIS frontend

A277469 E.g.f.: arcsin(x)/(1 + LambertW(-x)).

0, 1, 2, 13, 112, 1329, 19344, 336533, 6778752, 155247777, 3980956800, 112984562813, 3515475849216, 118984054897681, 4351800687259648, 171034439586509445, 7188243684485414912, 321696219477456836929, 15273278824827215388672, 766732102664665113137517

Offset: 0

Vaclav Kotesovec, Oct 16 2016

nonn

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

Cf. A000312, A086331, A277470.

CoefficientList[Series[ArcSin[x]/(1+LambertW[-x]), {x, 0, 25}], x] * Range[0, 25]!
Flatten[{0, Table[(1-(-1)^n)/2 * (n-2)!!^2 + Sum[Binomial[n, k] * (1-(-1)^k)/2 * (k-2)!!^2 * (n-k)^(n-k), {k, 1, n-1}], {n, 1, 25}]}] (* Vaclav Kotesovec, Oct 28 2016 *)

x='x+O('x^50); concat([0], Vec(serlaplace(asin(x)/(1 + lambertw(-x))))) \\ G. C. Greubel, Nov 07 2017

a(n) ~ arcsin(exp(-1)) * n^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

A277469 E.g.f.: arcsin(x)/(1 + LambertW(-x)).

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