A362671 - OEIS

%I #9 Apr 29 2023 09:09:34

%S 1,1,-1,10,-111,1716,-33755,807738,-22782207,740204776,-27226430739,

%T 1118416240470,-50750734988063,2521219487859372,-136098630522431499,

%U 7932551567421395866,-496501182232557828735,33214032504796887027408

%N E.g.f. satisfies A(x) = exp( x * exp(x) / A(x)^2 ).

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.

%F E.g.f.: exp( LambertW(2*x * exp(x))/2 ).

%F a(n) = Sum_{k=0..n} k^(n-k) * (-2*k+1)^(k-1) * binomial(n,k).

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(lambertw(2*x*exp(x))/2)))

%Y Cf. A273954, A360473, A362656, A362672.

%K sign

%O 0,4

%A _Seiichi Manyama_, Apr 29 2023