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

%I A268850 #9 Mar 03 2016 02:38:47
%S A268850 1,1,3431,397222288,460827731023773,2931247600219365331976,
%T A268850 70803267480031877368227941803,5078529731893937404909347067888886466,
%U A268850 909546798992441266072332791609067485208949369,358281333933096129012031117609647623312585201668494007
%N A268850 Number of sequences with 7 copies each of 1,2,...,n and longest increasing subsequence of length n.
%H A268850 Alois P. Heinz, <a href="/A268850/b268850.txt">Table of n, a(n) for n = 0..80</a>
%H A268850 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 A268850 a(n) ~ sqrt(7) * (7^7/6!)^n * n^(6*n) / exp(6*(n+1)). - _Vaclav Kotesovec_, Mar 03 2016
%t A268850 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 *)
%Y A268850 Row n=7 of A047909.
%K A268850 nonn
%O A268850 0,3
%A A268850 _Alois P. Heinz_, Feb 14 2016