A385948 a(0) = 1; a(n) = Sum_{k=0..n-1} binomial(k+6,6) * binomial(n-1,k) * a(k) * a(n-1-k).
1, 1, 8, 246, 21750, 4689546, 2197062708, 2046202234224, 3528088593902364, 10627093734265740672, 53295889303479275834616, 427383379745842299684115608, 5294446934064450139154214169992, 98355143996083993836475641916586304, 2669951662594756888115675117287929721248
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, binomial(j+6, 6)*binomial(i-1, j)*v[j+1]*v[i-j])); v;
Formula
E.g.f. A(x) satisfies A(x) = exp( Sum_{k=0..5} binomial(5,k) * x^(k+1)/(k+1)! * (d^k/dx^k A(x)) ), where (d^0/dx^0 A(x)) = A(x) by convention.