A277489 E.g.f.: -LambertW(-log(1+x)).

0, 1, 1, 5, 26, 224, 2244, 28496, 417976, 7122384, 136770960, 2937770472, 69626588976, 1806936836184, 50936933449752, 1550292926398680, 50661309325357824, 1769286989373994752, 65762170385201959680, 2591979585702305271552, 107982615297265761991680

Offset

0,4

Links

G. C. Greubel, Table of n, a(n) for n = 0..395

Formula

a(n) = Sum_{k=1..n} Stirling1(n, k)*k^(k-1).

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

Mathematica

CoefficientList[Series[-LambertW[-Log[1+x]], {x, 0, 20}], x] * Range[0, 20]!
Table[Sum[StirlingS1[n, k]*k^(k-1), {k, 1, n}], {n, 0, 20}]

Prog

(PARI) x='x+O('x^50); concat([0], Vec(serlaplace(-lambertw(-log(1+x))))) \\ G. C. Greubel, Jun 21 2017

Crossrefs

Cf. A001865, A052807, A133297.

Sequence in context: A007286 A305201 A099032 * A094652 A027529 A368294

Adjacent sequences: A277486 A277487 A277488 * A277490 A277491 A277492

Keyword

nonn

Author

Vaclav Kotesovec, Oct 17 2016

Status

approved