A385979 a(0) = 1; a(n) = Sum_{k=0..n-1} (k+1) * binomial(k+2,2) * binomial(n-1,k) * a(k) * a(n-1-k).
1, 1, 7, 145, 6449, 522096, 69506737, 14186121706, 4212887224905, 1747635451186240, 979909591959562571, 722787600597422326704, 685585597413868516073953, 820283211774547803576454720, 1217648676024408903145299884925, 2210504358495882876855897821031376
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+2, 2)*binomial(i-1, j)*v[j+1]*v[i-j])); v;
Formula
E.g.f. A(x) satisfies A(x) = exp( Sum_{k=0..2} binomial(2,k) * x^(k+1)/k! * (d^k/dx^k A(x)) ), where (d^0/dx^0 A(x)) = A(x) by convention.