%I #20 Oct 21 2021 08:54:36

%S -1,3,1,27,289,4683,95761,2382747,69870529,2359997163,90239163121,

%T 3853391348667,181765659243169,9386568200722443,526713953100688081,

%U 31912283163641549787,2076293242327577102209,144382074825232693748523,10686433228580787658046641

%N a(n) = (-5*(-1)^n + Sum_{k>=0} 2*A000108(k)*k^n/5^k)/sqrt(5), where A000108 are Catalan numbers.

%H Vaclav Kotesovec, <a href="/A260902/b260902.txt">Table of n, a(n) for n = 0..100</a>

%F a(n) ~ 2^(3/2) * n^(n-1) / (sqrt(5) * exp(n) * log(5/4)^(n-1/2)).

%F E.g.f.: -sqrt( exp(-x) * (-4+5*exp(-x)) ). - _Seiichi Manyama_, Oct 21 2021

%t Table[(-5*(-1)^n + Sum[2*CatalanNumber[k] k^n/5^k, {k, 0, Infinity}]) / Sqrt[5], {n, 0, 20}]

%o (PARI) N=20; x='x+O('x^N); Vec(serlaplace(-sqrt(exp(-x)*(-4+5*exp(-x))))) \\ _Seiichi Manyama_, Oct 21 2021

%Y Cf. A000108, A260701, A348468.

%K sign

%O 0,2

%A _Vaclav Kotesovec_, Nov 17 2015