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 A381480 #10 Feb 25 2025 01:59:05
%S A381480 1,2,14,174,3168,76450,2304720,83473726,3533382272,171254814210,
%T A381480 9355068840960,568799458870478,38102773549750272,2788540163472852386,
%U A381480 221380225364522119168,18950242574522637197790,1739955233454599038402560,170582215179135413189856514,17785491645892269582026145792
%N A381480 E.g.f. A(x) satisfies A(x) = 1/( 1 - x * A(x) * cos(x * A(x)) )^2.
%C A381480 As stated in the comment of A185951, A185951(n,0) = 0^n.
%F A381480 E.g.f.: B(x)^2, where B(x) is the e.g.f. of A381479.
%F A381480 a(n) = 2 * Sum_{k=0..n} k! * binomial(2*n+k+2,k)/(2*n+k+2) * i^(n-k) * A185951(n,k), where i is the imaginary unit.
%F A381480 E.g.f.: (1/x) * Series_Reversion( x*(1 - x*cos(x))^2 ).
%o A381480 (PARI) a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
%o A381480 a(n) = 2*sum(k=0, n, k!*binomial(2*n+k+2, k)/(2*n+k+2)*I^(n-k)*a185951(n, k));
%Y A381480 Cf. A185951, A381478.
%K A381480 nonn
%O A381480 0,2
%A A381480 _Seiichi Manyama_, Feb 24 2025