A268853 Number of sequences with 10 copies each of 1,2,...,n and longest increasing subsequence of length n.

1, 1, 184755, 5549991941777, 4697818999010952011441, 47964531978782851644184417448714, 3553102771891168237056005934820411063204249, 1355554085495648757684163048897568469564674091083870680, 2077847308887546704733072843165544143697549966176523511722695300153

Offset: 0

Author

Alois P. Heinz, Feb 14 2016

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..60
• J. D. Horton and A. Kurn, Counting sequences with complete increasing subsequences, Congressus Numerantium, 33 (1981), 75-80. MR 681905

Crossrefs

Row n=10 of A047909.

Programs

Mathematica

Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[k!/(i1!*i2!*i3!*i4!*i5!*i6!* i7!*i8!*i9!*(k - i1 - i2 - i3 - i4 - i5 - i6 - i7 - i8 - i9)!)*(10*k)!/(i1 + 2*i2 + 3*i3 + 4*i4 + 5*i5 + 6*i6 + 7*i7 + 8*i8 + 9*i9 + 10*(k - i1 - i2 - i3 - i4 - i5 - i6 - i7 - i8 - i9))!*(-1)^(i1 + 2*i2 + 3*i3 + 4*i4 + 5*i5 + 6*i6 + 7*i7 + 8*i8 + 9*i9 + 10*(k - i1 - i2 - i3 - i4 - i5 - i6 - i7 - i8 - i9) - k)/(9!^i1 * 8!^i2 * 7!^i3 * 6!^i4 * 5!^i5 * 4!^i6 * 3!^i7 * 2!^i8), {i9, 0, k - i1 - i2 - i3 - i4 - i5 - i6 - i7 - i8}], {i8, 0, k - i1 - i2 - i3 - i4 - i5 - i6 - i7}], {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(10) * (10^10/9!)^n * n^(9*n) / exp(9*(n+1)). - Vaclav Kotesovec, Mar 03 2016