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 A381379 #11 Feb 22 2025 09:55:53
%S A381379 1,2,6,18,-48,-2630,-52800,-824054,-8682240,54462258,7410631680,
%T A381379 305163480578,8935815871488,167137193150954,-1440976761090048,
%U A381379 -349400091225243270,-22113174143289262080,-960586728800597050526,-26252145855684866211840,255024367557922004307442
%N A381379 E.g.f. A(x) satisfies A(x) = 1/( 1 - x * cos(x * A(x)) )^2.
%C A381379 As stated in the comment of A185951, A185951(n,0) = 0^n.
%F A381379 E.g.f.: B(x)^2, where B(x) is the e.g.f. of A381378.
%F A381379 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.
%o A381379 (PARI) a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
%o A381379 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 A381379 Cf. A185951, A381378.
%K A381379 sign
%O A381379 0,2
%A A381379 _Seiichi Manyama_, Feb 22 2025