A385985 a(0) = 1; a(n) = Sum_{k=0..n-1} (2^k + 1) * binomial(n-1,k) * a(k) * a(n-1-k).
1, 2, 10, 94, 1514, 40790, 1862050, 148965310, 21742138970, 5994070800710, 3197362825740850, 3348408098259631150, 6941708283693589284650, 28621208382355252313372150, 235296246090820978083474438850, 3862393961855717768080204865278750, 126690441172711092666839985418516720250
Offset: 0
Keywords
Programs
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PARI
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, i-1, (2^j+1)*binomial(i-1, j)*v[j+1]*v[i-j])); v;
Formula
E.g.f. A(x) satisfies A'(x) = A(x) * (A(x) + A(2*x)).