A277485 E.g.f.: -exp(2*x)*LambertW(-x).

0, 1, 6, 33, 216, 1865, 21228, 303765, 5222864, 104540337, 2383558740, 60933722069, 1725392415288, 53590463856345, 1811281159509500, 66172416761172885, 2598298697830360992, 109116931783034360801, 4880122696811960470692, 231565260558289051906965

Offset

0,3

Links

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

Formula

a(n) = Sum_{m=1..n} (binomial(n,m) * Sum_{k=1..m} binomial(m,k)*k^(k-1)).

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

Mathematica

CoefficientList[Series[-Exp[2*x]*LambertW[-x], {x, 0, 20}], x]*Range[0, 20]!
Table[Sum[Binomial[n, m]*Sum[Binomial[m, k]*k^(k-1), {k, 1, m}], {m, 1, n}], {n, 0, 20}]

Prog

(PARI) x='x+O('x^50); concat([0], Vec(serlaplace(- exp(2*x)*lambertw(-x) ))) \\ G. C. Greubel, Nov 08 2017

Crossrefs

Cf. A000169, A069856, A086331, A277457, A277473, A277474.

Sequence in context: A193665 A097662 A366200 * A012522 A012326 A277260

Adjacent sequences: A277482 A277483 A277484 * A277486 A277487 A277488

Keyword

nonn

Author

Vaclav Kotesovec, Oct 17 2016

Status

approved