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 A379879 #16 Jan 23 2025 04:34:20
%S A379879 1,0,1,5,41,439,5869,94275,1770705,38102255,924580181,24984120523,
%T A379879 744154938361,24224671103463,855748556756157,32604902612628419,
%U A379879 1332864500919743393,58192519232324179423,2702582455278623736997,133037424985668849756603
%N A379879 E.g.f. A(x) satisfies A(x) = exp(-x) + x*A(x)^2.
%F A379879 E.g.f.: 2*exp(-x)/(1 + sqrt(1 - 4*x*exp(-x))).
%F A379879 a(n) = -n! * Sum_{k=0..n} (-k-1)^(n-k-1) * binomial(2*k,k)/(n-k)!.
%F A379879 a(n) ~ sqrt(1 + LambertW(-1/4)) * n^(n-1) / (2^(3/2) * (-LambertW(-1/4))^(n+1) * exp(n)). - _Vaclav Kotesovec_, Jan 23 2025
%o A379879 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(2*exp(-x)/(1+sqrt(1-4*x*exp(-x)))))
%o A379879 (PARI) a(n) = -n!*sum(k=0, n, (-k-1)^(n-k-1)*binomial(2*k, k)/(n-k)!);
%Y A379879 Cf. A000166, A379878.
%Y A379879 Cf. A377859, A379868.
%K A379879 nonn
%O A379879 0,4
%A A379879 _Seiichi Manyama_, Jan 05 2025