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 A381142 #11 Feb 16 2025 08:34:07
%S A381142 1,1,3,15,113,1137,14355,218239,3883585,79218721,1822842243,
%T A381142 46717337007,1319891043569,40759239427857,1365932381706963,
%U A381142 49373610759452575,1914856819983977473,79316216447375396161,3494800326874932467331,163218136611270923087439
%N A381142 Expansion of e.g.f. exp( -LambertW(-sin(x)) ).
%H A381142 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A381142 E.g.f. A(x) satisfies A(x) = exp( sin(x) * A(x) ).
%F A381142 a(n) = Sum_{k=0..n} (k+1)^(k-1) * i^(n-k) * A136630(n,k), where i is the imaginary unit.
%o A381142 (PARI) a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
%o A381142 a(n) = sum(k=0, n, (k+1)^(k-1)*I^(n-k)*a136630(n, k));
%Y A381142 Cf. A002017, A381145, A381148.
%Y A381142 Cf. A136630, A185690, A277498.
%K A381142 nonn
%O A381142 0,3
%A A381142 _Seiichi Manyama_, Feb 15 2025