A368439 Expansion of e.g.f. exp(x) / (4 - 3*exp(2*x)).
1, 7, 97, 2023, 56257, 1955527, 81570337, 3969606823, 220777431937, 13813838801287, 960354511044577, 73441487204670823, 6126887497334519617, 553733062241471461447, 53894653951229272883617, 5620230710788836168938023, 625160202763025501303191297
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+3*sum(j=1, i, 2^j*binomial(i, j)*v[i-j+1])); v;
Formula
a(n) = 1 + 3 * Sum_{k=1..n} 2^k * binomial(n,k) * a(n-k).