This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A268847 #22 Mar 03 2016 03:35:42
%S A268847 1,1,69,31451,46922017,162588279629,1077273394836829,
%T A268847 12084070123028603391,211301962987912098409729,
%U A268847 5426679072605204732028894233,195676681342450229063393365876181,9562449832974304724626743446267704131,615516610914323638585463757154352054695009
%N A268847 Number of sequences with 4 copies each of 1,2,...,n and longest increasing subsequence of length n.
%H A268847 Alois P. Heinz and Vaclav Kotesovec, <a href="/A268847/b268847.txt">Table of n, a(n) for n = 0..145</a> (terms 0..70 from Alois P. Heinz)
%H A268847 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 A268847 a(n) ~ 2^(7*n+1) * n^(3*n) / (3^n * exp(3*n+3)). - _Vaclav Kotesovec_, Feb 21 2016
%F A268847 Recurrence: 81*(n-4)*(n-3)^2*(n-2)^3*a(n) = 27*(n-4)*(n-3)^2*(57*n^7 - 328*n^6 + 560*n^5 + 159*n^4 - 1591*n^3 + 1942*n^2 - 994*n + 192)*a(n-1) - 18*(n-4)*(n-1)^3*(2*n - 3)*(4*n - 7)*(4*n - 5)*(18*n^7 - 111*n^6 - 76*n^5 + 2183*n^4 - 6887*n^3 + 9632*n^2 - 6371*n + 1620)*a(n-2) + 24*(n-2)^3*(n-1)^4*(2*n - 5)*(2*n - 3)*(4*n - 11)*(4*n - 9)*(4*n - 7)*(4*n - 5)*(n^5 + 6*n^4 - 115*n^3 + 440*n^2 - 626*n + 288)*a(n-3) - 32*(n-3)^3*(n-2)^4*(n-1)^5*(2*n - 7)*(2*n - 5)*(2*n - 3)*(4*n - 15)*(4*n - 13)*(4*n - 11)*(4*n - 9)*(4*n - 7)*(4*n - 5)*a(n-4). - _Vaclav Kotesovec_, Mar 03 2016
%e A268847 a(2) = binomial(8,4) - 1 = 69 because there are binomial(8,4) = 70 sequences with 4 copies of 1 and 4 copies of 2 and only 22221111 does not have an increasing subsequence of length 2.
%t A268847 Table[Sum[Sum[Sum[k!/(i1!*i2!*i3!*(k - i1 - i2 - i3)!)*(4*k)!/(i1 + 2*i2 + 3*i3 + 4*(k - i1 - i2 - i3))!*(-1)^(i1 + 2*i2 + 3*i3 + 4*(k - i1 - i2 - i3) - k)/(6^i1*2^i2), {i3, 0, k - i1 - i2}], {i2, 0, k - i1}], {i1, 0, k}], {k, 0, 20}] (* _Vaclav Kotesovec_, Mar 02 2016, after Horton and Kurn *)
%Y A268847 Row n=4 of A047909.
%K A268847 nonn
%O A268847 0,3
%A A268847 _Alois P. Heinz_, Feb 14 2016