A268850 Number of sequences with 7 copies each of 1,2,...,n and longest increasing subsequence of length n.

1, 1, 3431, 397222288, 460827731023773, 2931247600219365331976, 70803267480031877368227941803, 5078529731893937404909347067888886466, 909546798992441266072332791609067485208949369, 358281333933096129012031117609647623312585201668494007

Offset: 0

Author

Alois P. Heinz, Feb 14 2016

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..80
• J. D. Horton and A. Kurn, Counting sequences with complete increasing subsequences, Congressus Numerantium, 33 (1981), 75-80. MR 681905

Crossrefs

Row n=7 of A047909.

Programs

Mathematica

Table[Sum[Sum[Sum[Sum[Sum[Sum[k!/(i1!*i2!*i3!*i4!*i5!*i6!*(k - i1 - i2 - i3 - i4 - i5 - i6)!)*(7*k)!/(i1 + 2*i2 + 3*i3 + 4*i4 + 5*i5 + 6*i6 + 7*(k - i1 - i2 - i3 - i4 - i5 - i6))!*(-1)^(i1 + 2*i2 + 3*i3 + 4*i4 + 5*i5 + 6*i6 + 7*(k - i1 - i2 - i3 - i4 - i5 - i6) - k)/(720^i1*120^i2*24^i3*6^i4*2^i5), {i6, 0, k - i1 - i2 - i3 - i4 - i5}], {i5, 0, k - i1 - i2 - i3 - i4}], {i4, 0, k - i1 - i2 - i3}], {i3, 0, k - i1 - i2}], {i2, 0, k - i1}], {i1, 0, k}], {k, 0, 10}] (* Vaclav Kotesovec, Mar 02 2016, after Horton and Kurn *)

Formula

a(n) ~ sqrt(7) * (7^7/6!)^n * n^(6*n) / exp(6*(n+1)). - Vaclav Kotesovec, Mar 03 2016