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 A369921 #21 Feb 08 2024 16:14:25
%S A369921 0,0,2,18,204,2940,56670,1471806,52067512,2520298584,167850357210,
%T A369921 15435027907530,1967345286257604,348527628228821652,
%U A369921 86057693880611800438,29677160119074814383030,14321851348104417100842480
%N A369921 Number of cover relations summed over the rank-1 labeled posets on [n].
%C A369921 The rank of a poset is the number of cover relations in a maximal chain.
%C A369921 A cover relation in a poset is an ordered pair x <= y such that there is no z with x <= z <= y.
%H A369921 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CoverRelation.html">Cover Relation</a>.
%F A369921 a(n) = Sum_{k=1..floor(n^2/4)} A052296(n,k)*k.
%t A369921 nn = 16; Table[Table[n!, {n, 0, nn}] CoefficientList[D[Series[Sum[Exp[y x]^Binomial[n, i]*Exp[ x]^(2^n - Binomial[n, i] - 1) x^n/n!, {n, 0, nn}], {x, 0, nn}], y] /. y -> 1, x]*i, {i, 1, nn - 1}] // Total
%Y A369921 Cf. A001831, A369919, A052296.
%K A369921 nonn
%O A369921 0,3
%A A369921 _Geoffrey Critzer_, Feb 05 2024