A385875 a(n) = 1 + Sum_{k=0..n-1} binomial(k+2,3) * a(k) * a(n-1-k).
1, 1, 2, 10, 111, 2347, 84757, 4837213, 411373408, 49787445476, 8265626303452, 1826809978098228, 524311794034090050, 191377585766768936606, 87269255118865044728501, 48958442598180565027265909, 33340876732769115354996751746, 27239595466972699678481509900786
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+sum(j=0, i-1, binomial(j+2, 3)*v[j+1]*v[i-j])); v;
Formula
G.f. A(x) satisfies A(x) = 1/( (1 - x) * ( 1 - x*Sum_{k=1..3} binomial(2,k-1) * x^k/k! * (d^k/dx^k A(x)) ) ).