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 A381261 #9 Feb 18 2025 08:57:22
%S A381261 1,1,5,46,669,13176,328153,9889328,349998169,14232282112,653960139021,
%T A381261 33511444515968,1894938691013173,117209395966704640,
%U A381261 7872535432641217185,570622024676568564736,44395462114163659522353,3690312836780077587120128,326399124496126009678138261
%N A381261 Expansion of e.g.f. exp( -LambertW(-2 * x * cos(x)) / 2 ).
%C A381261 As stated in the comment of A185951, A185951(n,0) = 0^n.
%F A381261 E.g.f. A(x) satisfies A(x) = exp( x * cos(x) * A(x)^2 ).
%F A381261 a(n) = Sum_{k=0..n} (2*k+1)^(k-1) * i^(n-k) * A185951(n,k), where i is the imaginary unit.
%o A381261 (PARI) a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
%o A381261 a(n) = sum(k=0, n, (2*k+1)^(k-1)*I^(n-k)*a185951(n, k));
%Y A381261 Cf. A185951, A381141.
%K A381261 nonn
%O A381261 0,3
%A A381261 _Seiichi Manyama_, Feb 18 2025