A365110 G.f. satisfies A(x) = 1 + x / (1 + x*A(x))^3.
1, 1, -3, 3, 11, -54, 66, 297, -1575, 1980, 10300, -55392, 68352, 403583, -2153685, 2551845, 16999045, -89142087, 99986901, 750955382, -3850437018, 4041467331, 34310059311, -171533033904, 166630375248, 1607168518073, -7821913867611, 6950050797297
Offset: 0
Keywords
Programs
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PARI
a(n, s=3) = sum(k=0, n, (-1)^(n-k)*binomial(n-k+1, k)*binomial(n+(s-1)*k-1, n-k)/(n-k+1));
Formula
If g.f. satisfies A(x) = 1 + x/(1 + x*A(x))^s, then a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n-k+1,k) * binomial(n+(s-1)*k-1,n-k)/(n-k+1).