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%I #13 Mar 02 2016 20:47:17
%S 1,1,923,16928840,2176464012941,1162145520205261219,
%T 1878320344216429026862153,7465237877942551321425443305798,
%U 63178476289432401423971737795658030945,1025794060996626005769021866749636185341527229,29539005031390270063835072245497576346701114916209911
%N Number of sequences with 6 copies each of 1,2,...,n and longest increasing subsequence of length n.
%H Vaclav Kotesovec and Alois P. Heinz, <a href="/A268849/b268849.txt">Table of n, a(n) for n = 0..97</a> (terms n=0..34 from Vaclav Kotesovec)
%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) ~ 2^(3*n + 1/2) * 3^(5*n + 1/2) * n^(5*n) / (5^n * exp(5*(n+1))). - _Vaclav Kotesovec_, Feb 21 2016
%t Table[Sum[Sum[Sum[Sum[Sum[k!/(i1!*i2!*i3!*i4!*i5!*(k - i1 - i2 - i3 - i4 - i5)!)*(6*k)!/(i1 + 2*i2 + 3*i3 + 4*i4 + 5*i5 + 6*(k - i1 - i2 - i3 - i4 - i5))!*(-1)^(i1 + 2*i2 + 3*i3 + 4*i4 + 5*i5 + 6*(k - i1 - i2 - i3 - i4 - i5) - k)/(120^ i1*24^i2*6^i3*2^i4), {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=6 of A047909.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Feb 14 2016
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