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Expansion of e.g.f. exp(-x * sqrt(1-4*x)).
2

%I #11 Apr 10 2023 10:51:57

%S 1,-1,5,-1,121,1039,20221,416975,10573361,309650399,10335294901,

%T 386839539679,16045117551145,730346985279599,36191355037097261,

%U 1939288174467052079,111724538085236200801,6886112439557645126335,452112545350761238085221

%N Expansion of e.g.f. exp(-x * sqrt(1-4*x)).

%F a(n) = (-1)^n * n! * Sum_{k=0..n} 4^k * binomial((n-k)/2,k)/(n-k)!.

%F a(n) ~ 2^(2*n - 5/2) * n^(n-1) / exp(n). - _Vaclav Kotesovec_, Apr 10 2023

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-x*sqrt(1-4*x))))

%Y Cf. A362158.

%K sign,easy

%O 0,3

%A _Seiichi Manyama_, Apr 10 2023