A386510 a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-1} (1 + k) * binomial(k+1,2) * binomial(n-1,k) * a(k) * a(n-1-k).
1, 1, 3, 34, 949, 52421, 5050711, 779516095, 181069531665, 60337677803905, 27766510630927741, 17108421087708824831, 13757393965653865220629, 14130398908817131991819653, 18201370833558663815315691987, 28941823262680770630349968403381, 56033750665620660972762531436196641
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]=v[i]+sum(j=0, i-1, (1+j)*binomial(j+1, 2)*binomial(i-1, j)*v[j+1]*v[i-j])); v;
Formula
E.g.f. A(x) satisfies A(x) = exp( x + x^2 * (d/dx A(x)) + x^3/2 * (d^2/dx^2 A(x)) ).