A386300 a(n) = 1 + Sum_{k=0..n-1} (-1)^k * binomial(n-1,k) * a(k) * a(n-1-k).
1, 2, 1, -5, 1, 89, 1, -2603, 1, 133265, 1, -10449779, 1, 1161734969, 1, -173838018059, 1, 33692909616161, 1, -8210919096355811, 1, 2457354686029706057, 1, -886023132463389334523, 1, 378811390242562021309361, 1, -189490246977278296495043411, 1, 109640147405400620012620910681
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]=1+sum(j=0, i-1, (-1)^j*binomial(i-1, j)*v[j+1]*v[i-j])); v;
Formula
E.g.f. A(x) satisfies A'(x) = exp(x) + A(x) * A(-x).
a(2*n) = 1 for n >= 0.