This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A386502 #13 Jul 24 2025 09:31:32
%S A386502 1,1,1,1,25,3121,1141921,967142401,1632504592321,4951351715986369,
%T A386502 25004252825639317441,198308457113999900437441,
%U A386502 2358282522829655305887600961,40498770303734530275747011026561,973509226030256545543333641850364737,31906760631850274511535853878168004240641
%N A386502 E.g.f. A(x) satisfies A(x) = exp(x + x^4*A'''(x)).
%F A386502 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).
%F A386502 a(n) == 1 (mod 24). - _Hugo Pfoertner_, Jul 24 2025
%o A386502 (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;
%Y A386502 Cf. A143925, A385066, A386503, A386504.
%Y A386502 Cf. A385921, A386449.
%K A386502 nonn
%O A386502 0,5
%A A386502 _Seiichi Manyama_, Jul 24 2025