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 A381305 #8 Feb 20 2025 08:39:42
%S A381305 1,1,0,-1,-4,1,32,181,-192,-4919,-31616,88571,2089984,13830545,
%T A381305 -83841024,-1884928471,-11874992128,142704083281,3085703610368,
%U A381305 16806597846295,-397246640947200,-8257973126103359,-32717082633175040,1686557057210338589,33490001971564773376
%N A381305 E.g.f. A(x) satisfies A(x) = 1/( 1 - sin(x * A(x)^(1/2)) / A(x)^(3/2) ).
%F A381305 a(n) = Sum_{k=0..n} k! * binomial(n/2-k/2+1,k)/(n/2-k/2+1) * i^(n-k) * A136630(n,k), where i is the imaginary unit.
%o A381305 (PARI) a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
%o A381305 a(n) = sum(k=0, n, k!*binomial(n/2-k/2+1, k)/(n/2-k/2+1)*I^(n-k)*a136630(n, k));
%Y A381305 Cf. A136630.
%K A381305 sign
%O A381305 0,5
%A A381305 _Seiichi Manyama_, Feb 19 2025