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Expansion of e.g.f. 1/(1 - exp(x) + exp(3*x)).
0

%I #9 Dec 08 2023 09:57:12

%S 1,-2,0,22,-48,-722,5160,39142,-731808,-1875362,138079320,-428616938,

%T -32571174768,360902614798,8748630825480,-218739750924218,

%U -2165282730308928,135578968355309758,-45942716160492360,-89526354705694434698,1011199293695966345712

%N Expansion of e.g.f. 1/(1 - exp(x) + exp(3*x)).

%F a(0) = 1; a(n) = Sum_{k=1..n} (1 - 3^k) * binomial(n,k) * a(n-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, (1-3^j)*binomial(i, j)*v[i-j+1])); v;

%Y Cf. A355408, A355410.

%K sign

%O 0,2

%A _Seiichi Manyama_, Dec 08 2023