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 A385529 #10 Jul 02 2025 14:42:27
%S A385529 1,1,-5,-152,15949,6548656,-9510189137,-48598095401792,
%T A385529 849885323784381337,50192539805114962349824,
%U A385529 -9878895951508580401879879229,-6416836884643090722807370469927936,13640603845766595275775514993987722683941,94239467260528503337471761892783659993298198528
%N A385529 E.g.f. A(x) satisfies A(x) = exp(x*A(-3*x)).
%F A385529 a(0) = 1; a(n) = Sum_{k=0..n-1} (k+1) * (-3)^k * binomial(n-1,k) * a(k) * a(n-1-k).
%o A385529 (Ruby)
%o A385529 def ncr(n, r)
%o A385529 return 1 if r == 0
%o A385529 (n - r + 1..n).inject(:*) / (1..r).inject(:*)
%o A385529 end
%o A385529 def A(q, n)
%o A385529 ary = [1]
%o A385529 (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 A385529 ary
%o A385529 end
%o A385529 def A385529(n)
%o A385529 A(-3, n)
%o A385529 end
%Y A385529 Cf. A000272, A096538, A141369, A385526, A385527, A385528, A385530.
%Y A385529 Cf. A015098.
%K A385529 sign
%O A385529 0,3
%A A385529 _Seiichi Manyama_, Jul 02 2025