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 A385424 #15 Jun 28 2025 10:17:19
%S A385424 1,1,3,17,137,1465,19499,311873,5829073,124796081,3012319315,
%T A385424 80960234577,2398138520409,77630951407529,2726829925494011,
%U A385424 103300796618253825,4198494172961579169,182239547736082960737,8414068749731088539299,411754575622058760824593
%N A385424 Expansion of e.g.f. exp( -LambertW(-arcsin(x)) ).
%H A385424 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A385424 E.g.f. A(x) satisfies A(x) = exp( arcsin(x) * A(x) ).
%F A385424 a(n) = Sum_{k=0..n} (k+1)^(k-1) * A385343(n,k).
%F A385424 a(n) ~ n^(n-1) / (sqrt(cos(exp(-1))) * sin(exp(-1))^(n - 1/2) * exp(n - 3/2)). - _Vaclav Kotesovec_, Jun 28 2025
%o A385424 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-asin(x)))))
%Y A385424 Cf. A385426, A385427.
%Y A385424 Cf. A277502, A381142, A385343, A385425.
%K A385424 nonn
%O A385424 0,3
%A A385424 _Seiichi Manyama_, Jun 28 2025