A368014 Expansion of e.g.f. 1/(1 - exp(x) + exp(3*x)).
1, -2, 0, 22, -48, -722, 5160, 39142, -731808, -1875362, 138079320, -428616938, -32571174768, 360902614798, 8748630825480, -218739750924218, -2165282730308928, 135578968355309758, -45942716160492360, -89526354705694434698, 1011199293695966345712
Offset: 0
Keywords
Programs
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PARI
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, (1-3^j)*binomial(i, j)*v[i-j+1])); v;
Formula
a(0) = 1; a(n) = Sum_{k=1..n} (1 - 3^k) * binomial(n,k) * a(n-k).