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

%I #13 Dec 25 2023 10:02:19

%S 1,5,49,725,14305,352805,10441489,360526325,14226677185,631571457605,

%T 31152937452529,1690317145051925,100052040656540065,

%U 6415726051515362405,443047566486308303569,32780692416679034537525,2587108326603274903810945

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

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

%o (PARI) a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=1+2*sum(j=1, i, 2^j*binomial(i, j)*v[i-j+1])); v;

%Y Cf. A080253, A337026, A368439.

%Y Cf. A368442.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Dec 24 2023