A277489 - OEIS

%I #20 Sep 10 2024 04:27:58

%S 0,1,1,5,26,224,2244,28496,417976,7122384,136770960,2937770472,

%T 69626588976,1806936836184,50936933449752,1550292926398680,

%U 50661309325357824,1769286989373994752,65762170385201959680,2591979585702305271552,107982615297265761991680

%N Expansion of e.g.f. -LambertW(-log(1+x)).

%H G. C. Greubel, <a href="/A277489/b277489.txt">Table of n, a(n) for n = 0..395</a>

%H <a href="/index/Res#revert">Index entries for reversions of series</a>

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

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

%F E.g.f.: Series_Reversion( exp(x * exp(-x)) - 1 ). - _Seiichi Manyama_, Sep 10 2024

%t CoefficientList[Series[-LambertW[-Log[1+x]], {x, 0, 20}], x] * Range[0, 20]!

%t Table[Sum[StirlingS1[n, k]*k^(k-1), {k, 1, n}], {n, 0, 20}]

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

%Y Cf. A001865, A052807, A133297.

%Y Cf. A357337, A357338.

%K nonn

%O 0,4

%A _Vaclav Kotesovec_, Oct 17 2016