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%I #19 Nov 09 2017 09:27:28
%S 1,2,10,83,976,14957,283732,6433975,170054416,5139522809,174971556244,
%T 6629428776995,276781652752216,12628372294445221,625247682269320156,
%U 33391212230179659503,1913456535998407683616,117119224411257276521585
%N Expansion of -LambertW(LambertW(-x))/x.
%H Vincenzo Librandi, <a href="/A101878/b101878.txt">Table of n, a(n) for n = 0..100</a>
%F a(n) = Sum_{k=0..n} (k+1)^k*(n+1)^(n-k-1)*binomial(n, k).
%F a(n) ~ exp(1+exp(-1)+n*exp(-1)) / sqrt(1-exp(-1)) * n^(n-1). - _Vaclav Kotesovec_, Nov 27 2012
%t nn = 20; CoefficientList[Series[-LambertW[LambertW[-x]]/x, {x, 0, nn}], x]* Range[0, nn]! (* _Vaclav Kotesovec_, Nov 27 2012 *)
%o (PARI) x='x+O('x^50); Vec(serlaplace(-lambertw(lambertw(-x))/x)) \\ _G. C. Greubel_, Nov 08 2017
%o (PARI) a(n) = sum(k=0, n, (k+1)^k*(n+1)^(n-k-1)*binomial(n, k)); \\ _Michel Marcus_, Nov 09 2017
%K nonn
%O 0,2
%A _Vladeta Jovovic_, Jan 27 2005
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