A386299 a(n) = 1 + Sum_{k=0..n-1} 3^k * binomial(n-1,k) * a(k) * a(n-1-k).
1, 2, 9, 115, 3869, 349233, 88835413, 65934937157, 145194342935565, 955092851917410169, 18817250316042492760133, 1111535058740789497290819885, 196930668231818953760620540315069, 104661954649505883286587026252584631249, 166867787421063078832424708621648215185207669
Offset: 0
Keywords
Programs
-
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, 3^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(3*x).