A055531 Number of labeled order relations on n nodes in which longest chain has 2 nodes.

2, 12, 86, 840, 11642, 227892, 6285806, 243593040, 13262556722, 1014466283292, 109128015915206, 16521353903210520, 3524056001906654762, 1059868947134489801412, 449831067019305308555486, 269568708630308018001547680, 228228540531327778410439620962

Offset: 2

Author

N. J. A. Sloane, Jul 10 2000

Keywords

• easy
• nonn

References

• L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 60.

Crossrefs

A column or diagonal of triangle in A342587.

Cf. A001831, A052296.

Formula

a(n) = A001831(n)-1.

a(n) = Sum_{k=1..n-1} binomial(n,k)*(2^(n-k)-1)^k. - Geoffrey Critzer, Oct 29 2023

Extensions

More terms from Vladeta Jovovic, Oct 24 2000

a(13)-a(16) corrected and more terms from Sean A. Irvine, Mar 25 2022