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 A381175 #10 Feb 16 2025 10:05:51
%S A381175 1,1,6,69,1224,29465,898320,33187133,1441200768,71956238769,
%T A381175 4061414246400,255737764687669,17773804761259008,1351494159065894857,
%U A381175 111608708333568036864,9947544079380663728685,951770403836914402099200,97301151510219112917218657,10585077723403580668983902208
%N A381175 E.g.f. A(x) satisfies A(x) = 1/( 1 - x * A(x)^2 * cos(x * A(x)) ).
%C A381175 As stated in the comment of A185951, A185951(n,0) = 0^n.
%F A381175 a(n) = Sum_{k=0..n} k! * binomial(n+2*k+1,k)/(n+2*k+1) * i^(n-k) * A185951(n,k), where i is the imaginary unit.
%o A381175 (PARI) a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
%o A381175 a(n) = sum(k=0, n, k!*binomial(n+2*k+1, k)/(n+2*k+1)*I^(n-k)*a185951(n, k));
%Y A381175 Cf. A381173, A381174, A381176.
%Y A381175 Cf. A364984, A381172.
%Y A381175 Cf. A185951.
%K A381175 nonn
%O A381175 0,3
%A A381175 _Seiichi Manyama_, Feb 16 2025