A268851 Number of sequences with 8 copies each of 1,2,...,n and longest increasing subsequence of length n.

1, 1, 12869, 9450343019, 98540942707986273, 7370846583668954571029069, 2612508237897293571677286548812861, 3315159778348807570604149155371730111763599, 12324197596430667064913735085330208112438377122058241

Offset: 0

Author

Alois P. Heinz, Feb 14 2016

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..70
• J. D. Horton and A. Kurn, Counting sequences with complete increasing subsequences, Congressus Numerantium, 33 (1981), 75-80. MR 681905

Crossrefs

Row n=8 of A047909.

Programs

Mathematica

Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[k!/(i1!*i2!*i3!*i4!*i5!*i6!*i7!*(k - i1 - i2 - i3 - i4 - i5 - i6 - i7)!)*(8*k)!/(i1 + 2*i2 + 3*i3 + 4*i4 + 5*i5 + 6*i6 + 7*i7 + 8*(k - i1 - i2 - i3 - i4 - i5 - i6 - i7))!*(-1)^(i1 + 2*i2 + 3*i3 + 4*i4 + 5*i5 + 6*i6 + 7*i7 + 8*(k - i1 - i2 - i3 - i4 - i5 - i6 - i7) - k)/(5040^i1 * 720^i2 * 120^i3 * 24^i4 * 6^i5 * 2^i6), {i7, 0, k - i1 - i2 - i3 - i4 - i5 - i6}], {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(8) * (8^8/7!)^n * n^(7*n) / exp(7*(n+1)). - Vaclav Kotesovec, Mar 03 2016