A386502 E.g.f. A(x) satisfies A(x) = exp(x + x^4*A'''(x)).
1, 1, 1, 1, 25, 3121, 1141921, 967142401, 1632504592321, 4951351715986369, 25004252825639317441, 198308457113999900437441, 2358282522829655305887600961, 40498770303734530275747011026561, 973509226030256545543333641850364737, 31906760631850274511535853878168004240641
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]=v[i]+sum(j=0, i-1, (1+j)*sum(k=1, 3, stirling(3, k, 1)*j^k)*binomial(i-1, j)*v[j+1]*v[i-j])); v;
Formula
a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-1} (1 + k) * (2*k - 3*k^2 + k^3) * binomial(n-1,k) * a(k) * a(n-1-k).
a(n) == 1 (mod 24). - Hugo Pfoertner, Jul 24 2025