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 A381384 #10 Feb 22 2025 09:55:43
%S A381384 1,1,2,5,0,-299,-5840,-90791,-1210496,-11174519,71397888,8367496301,
%T A381384 327020705792,9709296136541,226223975684096,2946493117173761,
%U A381384 -87437164233621504,-9675847870039338095,-535455805780063748096,-22518479178045130002731,-706013052362778282033152
%N A381384 E.g.f. A(x) satisfies A(x) = 1/( 1 - sin(x * A(x)^2) / A(x)^2 ).
%F A381384 a(n) = Sum_{k=0..n} k! * binomial(2*n-k+1,k)/(2*n-k+1) * i^(n-k) * A136630(n,k), where i is the imaginary unit.
%o A381384 (PARI) a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
%o A381384 a(n) = sum(k=0, n, k!*binomial(2*n-k+1, k)/(2*n-k+1)*I^(n-k)*a136630(n, k));
%Y A381384 Cf. A364980, A381376, A381378, A381382.
%Y A381384 Cf. A136630.
%K A381384 sign
%O A381384 0,3
%A A381384 _Seiichi Manyama_, Feb 22 2025