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 A385322 #16 Jul 25 2025 02:17:40
%S A385322 1,1,2,10,94,1386,29146,822928,29927612,1359897724,75429391276,
%T A385322 5013317213136,393252908602720,35947138247529952,3787896504780614864,
%U A385322 455830291523748797776,62132218311858089750416,9523376536749853754046864,1630878867943272798422352400,310238352508716702644975872192
%N A385322 E.g.f. A(x) satisfies A(x) = exp(x + x^2/2 * A'(x)).
%F A385322 a(0) = 1; a(n) = a(n-1) + (1/2) * Sum_{k=0..n-1} (1 + k) * k * binomial(n-1,k) * a(k) * a(n-1-k).
%o A385322 (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)*j*binomial(i-1, j)*v[j+1]*v[i-j])/2); v;
%Y A385322 Cf. A386531, A386532.
%Y A385322 Cf. A143925, A156325.
%K A385322 nonn
%O A385322 0,3
%A A385322 _Seiichi Manyama_, Jul 24 2025