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 A385283 #16 Jun 26 2025 08:09:05
%S A385283 1,1,3,3,-39,-775,-9045,-85813,-426447,7321329,325555155,7786757011,
%T A385283 137053423881,1388713844713,-21121997539461,-1827406866674085,
%U A385283 -69034283067822495,-1852635543265039903,-30574875232261547613,308376017794648053539,54871741689019890859065
%N A385283 Expansion of e.g.f. 1/(1 - 2 * x * cos(2*x))^(1/2).
%F A385283 a(n) = Sum_{k=0..n} A001147(k) * (2*i)^(n-k) * A185951(n,k), where i is the imaginary unit and A185951(n,0) = 0^n.
%o A385283 (PARI) a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
%o A385283 a001147(n) = prod(k=0, n-1, 2*k+1);
%o A385283 a(n) = sum(k=0, n, a001147(k)*(2*I)^(n-k)*a185951(n, k));
%Y A385283 Cf. A352252, A385284.
%Y A385283 Cf. A001586, A235134, A380155, A385281.
%Y A385283 Cf. A001147, A185951.
%K A385283 sign
%O A385283 0,3
%A A385283 _Seiichi Manyama_, Jun 24 2025