A386212 G.f. A(x) satisfies A(x) = 1/(1-x)^3 + x^2*A(x)*A'(x).
1, 3, 9, 37, 207, 1455, 12073, 113949, 1196499, 13778155, 172269777, 2321464773, 33524717911, 516428180631, 8453096463321, 146532991389613, 2682216423470763, 51706945300407315, 1047284621276095729, 22237895367773398821, 494041637873385734127, 11462206075715032723903
Offset: 0
Keywords
Programs
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PARI
a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=binomial(i+2, 2)+(i-1)/2*sum(j=0, i-1, v[j+1]*v[i-j])); v;
Formula
a(n) = binomial(n+2,2) + (n-1)/2 * Sum_{k=0..n-1} a(k) * a(n-1-k).
a(n) = binomial(n+2,2) + Sum_{k=0..n-1} k * a(k) * a(n-1-k).