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 A381388 #16 Feb 24 2025 08:00:33
%S A381388 1,1,6,71,1280,31201,961184,35838991,1569696768,79007365921,
%T A381388 4494170889472,285130996517399,19963494971809792,1529055924661457921,
%U A381388 127179971644212387840,11416028319985437309215,1099976414821996358795264,113239907265894992879189185,12404749306625020735299780608
%N A381388 E.g.f. A(x) satisfies A(x) = 1/( 1 - sin(x * A(x)^2) ).
%F A381388 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.
%F A381388 E.g.f.: ( (1/x) * Series_Reversion( x*(1 - sin(x))^2 ) )^(1/2).
%o A381388 (PARI) a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
%o A381388 a(n) = sum(k=0, n, k!*binomial(2*n+k+1, k)/(2*n+k+1)*I^(n-k)*a136630(n, k));
%Y A381388 Cf. A136630, A381389.
%K A381388 nonn
%O A381388 0,3
%A A381388 _Seiichi Manyama_, Feb 22 2025