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%I #16 Jul 01 2022 11:24:55
%S 1,2,16,170,2416,42962,916696,22819610,649207456,20778364322,
%T 738918769576,28905116527850,1233506128752496,57025618592932082,
%U 2839117599033828856,151446758367400488890,8617182795217834505536,520954229292164353554242
%N Expansion of e.g.f. 1/(1 + exp(x) - exp(3*x)).
%F a(0) = 1; a(n) = Sum_{k=1..n} (3^k - 1) * binomial(n,k) * a(n-k).
%F a(n) ~ n! / ((3 + 2*r) * log(r)^(n+1)), where r = 2*cosh(log((25 + 3*sqrt(69)) / 2) / 6)/sqrt(3). - _Vaclav Kotesovec_, Jul 01 2022
%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1+exp(x)-exp(3*x))))
%o (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, (3^j-1)*binomial(i, j)*v[i-j+1])); v;
%Y Cf. A000556, A355378, A355409.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Jul 01 2022
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