A368453 Expansion of e.g.f. 3*exp(x) / (4 - exp(3*x)).
1, 2, 8, 52, 452, 4892, 63508, 962012, 16654772, 324375292, 7019618708, 167098274972, 4339293330292, 122075401356092, 3698469101172308, 120054668185331932, 4156854586083305012, 152925374174876071292, 5956866331612558316308, 244927333201908131524892
Offset: 0
Keywords
Programs
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PARI
a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=1+sum(j=1, i, 3^(j-1)*binomial(i, j)*v[i-j+1])); v;
Formula
a(n) = 1 + Sum_{k=1..n} 3^(k-1) * binomial(n,k) * a(n-k).