A268853 - OEIS

%I #11 Mar 03 2016 02:41:45

%S 1,1,184755,5549991941777,4697818999010952011441,

%T 47964531978782851644184417448714,

%U 3553102771891168237056005934820411063204249,1355554085495648757684163048897568469564674091083870680,2077847308887546704733072843165544143697549966176523511722695300153

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

%H Alois P. Heinz, <a href="/A268853/b268853.txt">Table of n, a(n) for n = 0..60</a>

%H J. D. Horton and A. Kurn, Counting sequences with complete increasing subsequences, Congressus Numerantium, 33 (1981), 75-80. <a href="http://www.ams.org/mathscinet-getitem?mr=681905">MR 681905</a>

%F a(n) ~ sqrt(10) * (10^10/9!)^n * n^(9*n) / exp(9*(n+1)). - _Vaclav Kotesovec_, Mar 03 2016

%t 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 *)

%Y Row n=10 of A047909.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Feb 14 2016