A371889 G.f. A(x) satisfies A(x) = 1 - x/A(x)^2 * (1 - A(x) - A(x)^3).
1, 1, 2, 2, -1, -4, 7, 33, -5, -200, -151, 1185, 2202, -6069, -21799, 21791, 182718, 26520, -1349611, -1613331, 8674338, 21651795, -44750412, -217666394, 121538304, 1859974399, 1023915107, -13828122997, -23155237537, 86925632115, 282182920662
Offset: 0
Keywords
Programs
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PARI
a(n) = if(n==0, 1, sum(k=0, n, binomial(n, k)*binomial(n-3*k, n-k-1))/n);
Formula
a(n) = (1/n) * Sum_{k=0..n} binomial(n,k) * binomial(n-3*k,n-k-1) for n > 0.