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Expansion of e.g.f. exp(-x * (1 - x)^2) / (1 - x)^2.
1

%I #7 Aug 14 2024 23:14:12

%S 1,1,7,17,149,569,6019,34033,409513,3261041,42986591,451422641,

%T 6486586237,84605091817,1334440837339,20632779265169,358963187353169,

%U 6363955245003233,122111809463225143,2427035466387882961,51167058284040281701,1122982719058921672601

%N Expansion of e.g.f. exp(-x * (1 - x)^2) / (1 - x)^2.

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

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-x*(1-x)^2)/(1-x)^2))

%o (PARI) a(n) = (-1)^n*n!*sum(k=0, n, binomial(2*k-2, n-k)/k!);

%Y Cf. A375410, A375427.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Aug 14 2024