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 A381385 #11 Feb 22 2025 09:55:39
%S A381385 1,2,6,22,64,-398,-14768,-288458,-4695168,-62117470,-385004032,
%T A381385 15463485398,923640068096,33487329741842,957927747201024,
%U A381385 20185023268062070,95909717192212480,-21197461265149558718,-1619210077600334151680,-82170388240550451506282,-3226620083793471277105152
%N A381385 E.g.f. A(x) satisfies A(x) = 1/( 1 - sin(x * A(x)) / A(x) )^2.
%F A381385 E.g.f.: B(x)^2, where B(x) is the e.g.f. of A381384.
%F A381385 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.
%o A381385 (PARI) a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
%o A381385 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 A381385 Cf. A136630, A381384.
%K A381385 sign
%O A381385 0,2
%A A381385 _Seiichi Manyama_, Feb 22 2025