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

%I #8 Dec 08 2023 09:57:01

%S 1,-2,-4,14,144,286,-5080,-61058,-186144,4016958,73395928,468915102,

%T -4728823088,-167453193314,-2051810224568,-406640603074,

%U 533831885402048,11987797433266302,110763307665075640,-1459040819952150178,-80503810962755821904

%N Expansion of e.g.f. exp(exp(x) - exp(3*x)).

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

%o (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, (1-3^j)*binomial(i-1, j-1)*v[i-j+1])); v;

%Y Cf. A355378.

%K sign

%O 0,2

%A _Seiichi Manyama_, Dec 08 2023