%I #22 Oct 30 2023 15:32:22
%S 2,12,86,840,11642,227892,6285806,243593040,13262556722,1014466283292,
%T 109128015915206,16521353903210520,3524056001906654762,
%U 1059868947134489801412,449831067019305308555486,269568708630308018001547680,228228540531327778410439620962
%N Number of labeled order relations on n nodes in which longest chain has 2 nodes.
%D L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 60.
%F a(n) = A001831(n)-1.
%F a(n) = Sum_{k=1..n-1} binomial(n,k)*(2^(n-k)-1)^k. - _Geoffrey Critzer_, Oct 29 2023
%Y A column or diagonal of triangle in A342587.
%Y Cf. A001831, A052296.
%K easy,nonn
%O 2,1
%A _N. J. A. Sloane_, Jul 10 2000
%E More terms from _Vladeta Jovovic_, Oct 24 2000
%E a(13)-a(16) corrected and more terms from _Sean A. Irvine_, Mar 25 2022