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 A385530 #11 Jul 02 2025 14:42:21
%S A385530 1,1,-7,-359,90705,116586321,-715618113143,-20523234900205911,
%T A385530 2689857437569063003169,1586566688643256394542888225,
%U A385530 -4159073515698730238218108546470759,-47972197129364591236078587520718376138951,2414519164037893898620724924577882591112859773297
%N A385530 E.g.f. A(x) satisfies A(x) = exp(x*A(-4*x)).
%F A385530 a(0) = 1; a(n) = Sum_{k=0..n-1} (k+1) * (-4)^k * binomial(n-1,k) * a(k) * a(n-1-k).
%o A385530 (Ruby)
%o A385530 def ncr(n, r)
%o A385530 return 1 if r == 0
%o A385530 (n - r + 1..n).inject(:*) / (1..r).inject(:*)
%o A385530 end
%o A385530 def A(q, n)
%o A385530 ary = [1]
%o A385530 (1..n).each{|i| ary << (0..i - 1).inject(0){|s, j| s + (j + 1) * q ** j * ncr(i - 1, j) * ary[j] * ary[i - 1 - j]}}
%o A385530 ary
%o A385530 end
%o A385530 def A385530(n)
%o A385530 A(-4, n)
%o A385530 end
%Y A385530 Cf. A000272, A096538, A141369, A385526, A385527, A385528, A385529.
%Y A385530 Cf. A015099.
%K A385530 sign
%O A385530 0,3
%A A385530 _Seiichi Manyama_, Jul 02 2025