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 A381263 #8 Feb 18 2025 08:57:33
%S A381263 1,1,5,48,709,14152,356793,10882648,389790889,16040853568,
%T A381263 745908722477,38681745244032,2213527304014189,138556837227204736,
%U A381263 9417928265797994145,690818806495197538816,54391227913053881634001,4575388875753714015748096,409532433006878699321370197
%N A381263 Expansion of e.g.f. exp( -LambertW(-2 * sin(x)) / 2 ).
%F A381263 E.g.f. A(x) satisfies A(x) = exp( sin(x) * A(x)^2 ).
%F A381263 a(n) = Sum_{k=0..n} (2*k+1)^(k-1) * i^(n-k) * A136630(n,k), where i is the imaginary unit.
%o A381263 (PARI) a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
%o A381263 a(n) = sum(k=0, n, (2*k+1)^(k-1)*I^(n-k)*a136630(n, k));
%Y A381263 Cf. A136630, A381142.
%K A381263 nonn
%O A381263 0,3
%A A381263 _Seiichi Manyama_, Feb 18 2025