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Expansion of e.g.f. exp(-x * (1 - x)^2) / (1 - x)^3.
1

%I #7 Aug 14 2024 23:14:08

%S 1,2,11,50,349,2314,19903,173354,1796345,19428146,237268051,

%T 3061371202,43223040661,646504620410,10385505523079,176415362111354,

%U 3181608981134833,60451307924295394,1210235352100542235,25421507156298185426,559597201410003990221

%N Expansion of e.g.f. exp(-x * (1 - x)^2) / (1 - x)^3.

%F a(n) = (-1)^n * n! * Sum_{k=0..n} binomial(2*k-3,n-k)/k!.

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-x*(1-x)^2)/(1-x)^3))

%o (PARI) a(n) = (-1)^n*n!*sum(k=0, n, binomial(2*k-3, n-k)/k!);

%Y Cf. A375410, A375426.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Aug 14 2024