A385981 a(0) = 1; a(n) = Sum_{k=0..n-1} (k+1) * binomial(k+4,4) * binomial(n-1,k) * a(k) * a(n-1-k).
1, 1, 11, 526, 75981, 27017601, 20599793857, 30432196412318, 80590529100023889, 359767027014797719000, 2575966649397129017224661, 28392489655027195386265889544, 465411261102140455922541427819489, 11017701081052339904298545720453122836, 367264434033142995461894471693185212854475
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+4, 4)*binomial(i-1, j)*v[j+1]*v[i-j])); v;
Formula
E.g.f. A(x) satisfies A(x) = exp( Sum_{k=0..4} binomial(4,k) * x^(k+1)/k! * (d^k/dx^k A(x)) ), where (d^0/dx^0 A(x)) = A(x) by convention.