A385980 a(0) = 1; a(n) = Sum_{k=0..n-1} (k+1) * binomial(k+3,3) * binomial(n-1,k) * a(k) * a(n-1-k).
1, 1, 9, 295, 24921, 4504516, 1543745107, 919392117722, 890353538984905, 1330464112593541120, 2940642877993896450701, 9284167814032856189142864, 40666099850492306669400356041, 241073945237343019120798232332320, 1893421587381601800604423881821405775
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, (j+1)*binomial(j+3, 3)*binomial(i-1, j)*v[j+1]*v[i-j])); v;
Formula
E.g.f. A(x) satisfies A(x) = exp( Sum_{k=0..3} binomial(3,k) * x^(k+1)/k! * (d^k/dx^k A(x)) ), where (d^0/dx^0 A(x)) = A(x) by convention.