A147964 Number of consistent sets of 10 irreflexive binary order relationships over n objects.

120, 691020, 128047374, 6519340912, 156097542888, 2259242749800, 22815705739244, 175939638868224, 1099964624581680, 5812510584460580, 26753072198342490, 109684475412107232, 407515671392921520, 1390695205822539984, 4406577363489470616, 13079027432832437440

Offset: 5

Author

R. H. Hardin, May 04 2009

Keywords

• nonn
• easy

Links

• V. I. Rodionov, On the number of labeled acyclic digraphs, Discr. Math. 105 (1-3) (1992), 319-321.

Crossrefs

Related sequences for the number of consistent sets of k irreflexive binary order relationships over n objects: A147796 (k = 3), A147817 (k = 4), A147821 (k = 5), A147860 (k = 6), A147872 (k = 7), A147881 (k = 8), A147883 (k = 9).

Column k = 10 of A081064.

Programs

Mathematica

Table[(n - 4)*(n - 3)*(n - 2)*(n - 1)*n*(n^15 - 80*n^13 - 300*n^12 + 1366*n^11 + 18300*n^10 + 117700*n^9 + 293220*n^8 - 4873571*n^7 - 63731100*n^6 - 168619940*n^5 + 2528179320*n^4 + 17989477164*n^3 - 56994404400*n^2 - 561199055760*n + 1856094609600)/3628800, {n, 5, 20}] (* Wesley Ivan Hurt, Apr 12 2020 *)

Formula

a(n) = (n-4)*(n-3)*(n-2)*(n-1)*n*(n^15 - 80*n^13 - 300*n^12 + 1366*n^11 + 18300*n^10 + 117700*n^9 + 293220*n^8 - 4873571*n^7 - 63731100*n^6 - 168619940*n^5 + 2528179320*n^4 + 17989477164*n^3 - 56994404400*n^2 - 561199055760*n + 1856094609600)/3628800. - Vaclav Kotesovec, Apr 11 2020

Extensions

More terms from Vaclav Kotesovec, Apr 11 2020

Offset changed to n=5 by Petros Hadjicostas, Apr 11 2020