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 A385310 #17 Jun 26 2025 08:08:50
%S A385310 1,1,3,12,69,500,4455,46928,571977,7914384,122585355,2100940864,
%T A385310 39470867469,806555184448,17808628411119,422498774818560,
%U A385310 10717948285126545,289501146405400832,8295124400250875667,251300745071590317056,8025654235707259740885,269482309052945201181696
%N A385310 Expansion of e.g.f. 1/(1 - 2 * x * cos(x))^(1/2).
%F A385310 a(n) = Sum_{k=0..n} A001147(k) * i^(n-k) * A185951(n,k), where i is the imaginary unit and A185951(n,0) = 0^n.
%o A385310 (PARI) a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
%o A385310 a001147(n) = prod(k=0, n-1, 2*k+1);
%o A385310 a(n) = sum(k=0, n, a001147(k)*I^(n-k)*a185951(n, k));
%Y A385310 Cf. A352252, A385311.
%Y A385310 Cf. A380015, A385304, A385306, A385308.
%Y A385310 Cf. A001147, A185951, A352646, A385283.
%K A385310 nonn
%O A385310 0,3
%A A385310 _Seiichi Manyama_, Jun 24 2025