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

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

Offset

0,3

Links

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

Formula

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

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

Mathematica

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 *)

Prog

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

Crossrefs

Cf. A000169, A277470, A277473, A277483.

Sequence in context: A191691 A191712 A277475 * A005736 A354847 A123903

Adjacent sequences: A277481 A277482 A277483 * A277485 A277486 A277487

Keyword

nonn

Author

Vaclav Kotesovec, Oct 17 2016

Status

approved