A368455 Expansion of e.g.f. 3*exp(-x) / (4 - exp(3*x)).
1, 0, 4, 20, 180, 1940, 25204, 381780, 6609460, 128728340, 2785737204, 66312995540, 1722049711540, 48445655125140, 1467738434962804, 47643726641609300, 1649648835729498420, 60688474959603256340, 2363983970307953910004, 97199476595104080495060
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)^i+sum(j=1, i, 3^(j-1)*binomial(i, j)*v[i-j+1])); v;
Formula
a(n) = (-1)^n + Sum_{k=1..n} 3^(k-1) * binomial(n,k) * a(n-k).