%I #11 Jul 02 2022 09:27:56
%S 1,3,24,284,4476,88178,2084564,57493334,1812223276,64262620538,
%T 2531993864004,109738634393534,5188538157065276,265761817180172498,
%U 14659691726110341844,866403731832477234134,54619096812884242006476,3658454458052874579886058
%N Expansion of e.g.f. 1/(1 - Sum_{k=1..3} (exp(k*x) - 1)/k).
%F a(0) = 1; a(n) = Sum_{k=1..n} (1 + 2^(k-1) + 3^(k-1)) * binomial(n,k) * a(n-k).
%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-sum(k=1, 3, (exp(k*x)-1)/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+2^(j-1)+3^(j-1))*binomial(i, j)*v[i-j+1])); v;
%Y Column k=3 of A355427.
%Y Cf. A004701.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Jul 01 2022