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 A381285 #11 Jul 09 2025 10:14:30
%S A381285 1,1,2,2,-8,-104,-688,-3088,-128,209536,3145472,29795072,139389952,
%T A381285 -1715047424,-60056147968,-1004215072768,-10305404960768,
%U A381285 -1945682345984,2949643589844992,84438462955323392,1458284922371571712,12032890515685113856,-245515800089314459648
%N A381285 Expansion of e.g.f. 1/(1 - sin(2*x) / 2).
%F A381285 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} (-4)^k * binomial(n,2*k+1) * a(n-2*k-1).
%F A381285 a(n) = Sum_{k=0..n} k! * (2*i)^(n-k) * A136630(n,k), where i is the imaginary unit.
%t A381285 With[{nn=30},CoefficientList[Series[1/(1-Sin[2x]/2),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Jul 09 2025 *)
%o A381285 (PARI) a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
%o A381285 a(n) = sum(k=0, n, k!*(2*I)^(n-k)*a136630(n, k));
%Y A381285 Cf. A000111, A381286.
%Y A381285 Cf. A136630.
%K A381285 sign
%O A381285 0,3
%A A381285 _Seiichi Manyama_, Feb 18 2025