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A277473
E.g.f.: -exp(x)*LambertW(-x).
19
0, 1, 4, 18, 116, 1060, 12702, 187810, 3296120, 66897288, 1540762010, 39693752494, 1130866726596, 35300006582620, 1198036854980630, 43921652697277170, 1729775120233353968, 72831210167041246480, 3264674481128340280242, 155220967397580333229270
OFFSET
0,3
LINKS
FORMULA
a(n) = Sum_{k=1..n} binomial(n,k) * k^(k-1).
a(n) ~ exp(exp(-1)) * n^(n-1).
MATHEMATICA
CoefficientList[Series[-Exp[x]*LambertW[-x], {x, 0, 20}], x] * Range[0, 20]!
Table[Sum[Binomial[n, k]*k^(k-1), {k, 1, n}], {n, 0, 20}]
PROG
(PARI) x='x+O('x^50); concat([0], Vec(serlaplace(-exp(x)*lambertw(-x)))) \\ G. C. Greubel, Jun 11 2017
CROSSREFS
Partial sums of A038051.
Sequence in context: A220223 A137567 A326261 * A278994 A223008 A162224
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Oct 17 2016
STATUS
approved