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 A386503 #12 Jul 24 2025 09:31:56
%S A386503 1,1,1,1,1,121,87841,221971681,1493423016961,22593988839985921,
%T A386503 683468095232158346881,37898988106295372711276161,
%U A386503 3602374572375663444650415755521,556397556871212729711470761587498241,133676738300734051631377763872501373230081,48173754506706929414138973409107160269088573441
%N A386503 E.g.f. A(x) satisfies A(x) = exp(x + x^5*A''''(x)).
%F A386503 a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-1} (1 + k) * (-6*k + 11*k^2 - 6*k^3 + k^4) * binomial(n-1,k) * a(k) * a(n-1-k).
%F A386503 a(n) == 1 (mod 120). - _Hugo Pfoertner_, Jul 24 2025
%o A386503 (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, 4, stirling(4, k, 1)*j^k)*binomial(i-1, j)*v[j+1]*v[i-j])); v;
%Y A386503 Cf. A143925, A385066, A386502, A386504.
%Y A386503 Cf. A385922, A386450.
%K A386503 nonn
%O A386503 0,6
%A A386503 _Seiichi Manyama_, Jul 24 2025