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A268850 Number of sequences with 7 copies each of 1,2,...,n and longest increasing subsequence of length n. 3

%I

%S 1,1,3431,397222288,460827731023773,2931247600219365331976,

%T 70803267480031877368227941803,5078529731893937404909347067888886466,

%U 909546798992441266072332791609067485208949369,358281333933096129012031117609647623312585201668494007

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

%H Alois P. Heinz, <a href="/A268850/b268850.txt">Table of n, a(n) for n = 0..80</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(7) * (7^7/6!)^n * n^(6*n) / exp(6*(n+1)). - _Vaclav Kotesovec_, Mar 03 2016

%t 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 Row n=7 of A047909.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Feb 14 2016

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Last modified May 27 11:47 EDT 2022. Contains 354097 sequences. (Running on oeis4.)