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 A379688 #16 Jan 12 2025 10:17:28
%S A379688 1,2,20,366,9992,365130,16769292,929022206,60323670416,4494465562770,
%T A379688 378025706776340,35434198578761862,3663111561838580568,
%U A379688 414057463231218044186,50805545997014472821276,6725525908390393438264590,955435863749903677193184032,144987884255349864723586105122
%N A379688 Expansion of e.g.f. (1/x) * Series_Reversion( x * (1 - 2*x*exp(x)) ).
%H A379688 Seiichi Manyama, <a href="/A379688/b379688.txt">Table of n, a(n) for n = 0..326</a>
%F A379688 a(n) = (1/(n+1)) * Sum_{k=0..n} 2^(n-k) * (n-k)^k * (2*n-k)!/(k! * (n-k)!).
%F A379688 E.g.f. A(x) satisfies A(x) = 1/( 1 - 2*x*A(x)*exp(x*A(x)) ).
%F A379688 E.g.f.: B(x)^2, where B(x) is the e.g.f. of A380095.
%o A379688 (PARI) a(n) = sum(k=0, n, 2^(n-k)*(n-k)^k*(2*n-k)!/(k!*(n-k)!))/(n+1);
%Y A379688 Cf. A213644, A380097.
%Y A379688 Cf. A379659, A379687.
%Y A379688 Cf. A380095.
%K A379688 nonn
%O A379688 0,2
%A A379688 _Seiichi Manyama_, Dec 29 2024