A268849 Number of sequences with 6 copies each of 1,2,...,n and longest increasing subsequence of length n.

1, 1, 923, 16928840, 2176464012941, 1162145520205261219, 1878320344216429026862153, 7465237877942551321425443305798, 63178476289432401423971737795658030945, 1025794060996626005769021866749636185341527229, 29539005031390270063835072245497576346701114916209911

Offset: 0

Author

Alois P. Heinz, Feb 14 2016

Keywords

• nonn

Links

• Vaclav Kotesovec and Alois P. Heinz, Table of n, a(n) for n = 0..97 (terms n=0..34 from Vaclav Kotesovec)
• J. D. Horton and A. Kurn, Counting sequences with complete increasing subsequences, Congressus Numerantium, 33 (1981), 75-80. MR 681905

Crossrefs

Row n=6 of A047909.

Programs

Mathematica

Table[Sum[Sum[Sum[Sum[Sum[k!/(i1!*i2!*i3!*i4!*i5!*(k - i1 - i2 - i3 - i4 - i5)!)*(6*k)!/(i1 + 2*i2 + 3*i3 + 4*i4 + 5*i5 + 6*(k - i1 - i2 - i3 - i4 - i5))!*(-1)^(i1 + 2*i2 + 3*i3 + 4*i4 + 5*i5 + 6*(k - i1 - i2 - i3 - i4 - i5) - k)/(120^ i1*24^i2*6^i3*2^i4), {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) ~ 2^(3*n + 1/2) * 3^(5*n + 1/2) * n^(5*n) / (5^n * exp(5*(n+1))). - Vaclav Kotesovec, Feb 21 2016