A371890 G.f. A(x) satisfies A(x) = 1 - x/A(x)^3 * (1 - A(x) - A(x)^4).
1, 1, 2, 1, -4, 0, 37, 16, -313, -214, 3005, 2943, -30391, -39432, 318606, 522863, -3418205, -6889626, 37219105, 90415336, -408758113, -1183054415, 4505089166, 15442590040, -49599878555, -201138280510, 542949788652, 2614332298108, -5877502079248
Offset: 0
Keywords
Programs
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PARI
a(n) = if(n==0, 1, sum(k=0, n, binomial(n, k)*binomial(n-4*k, n-k-1))/n);
Formula
a(n) = (1/n) * Sum_{k=0..n} binomial(n,k) * binomial(n-4*k,n-k-1) for n > 0.