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 A381389 #16 Feb 24 2025 07:59:58
%S A381389 1,2,14,178,3344,83722,2628000,99358810,4398573568,223280915090,
%T A381389 12788876882176,816044058415298,57411735641690112,4415467258014111002,
%U A381389 368568207039291072512,33186631279383615035242,3206409506796711229521920,330893672854541429428877602
%N A381389 E.g.f. A(x) satisfies A(x) = 1/( 1 - sin(x * A(x)) )^2.
%F A381389 E.g.f.: B(x)^2, where B(x) is the e.g.f. of A381388.
%F A381389 a(n) = 2 * Sum_{k=0..n} k! * binomial(2*n+k+2,k)/(2*n+k+2) * i^(n-k) * A136630(n,k), where i is the imaginary unit.
%F A381389 E.g.f.: (1/x) * Series_Reversion( x*(1 - sin(x))^2 ).
%o A381389 (PARI) a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
%o A381389 a(n) = 2*sum(k=0, n, k!*binomial(2*n+k+2, k)/(2*n+k+2)*I^(n-k)*a136630(n, k));
%Y A381389 Cf. A136630, A381388.
%K A381389 nonn
%O A381389 0,2
%A A381389 _Seiichi Manyama_, Feb 22 2025