cp's OEIS Frontend

A268851 Number of sequences with 8 copies each of 1,2,...,n and longest increasing subsequence of length n.

%I A268851 #9 Mar 03 2016 02:39:51
%S A268851 1,1,12869,9450343019,98540942707986273,7370846583668954571029069,
%T A268851 2612508237897293571677286548812861,
%U A268851 3315159778348807570604149155371730111763599,12324197596430667064913735085330208112438377122058241
%N A268851 Number of sequences with 8 copies each of 1,2,...,n and longest increasing subsequence of length n.
%H A268851 Alois P. Heinz, <a href="/A268851/b268851.txt">Table of n, a(n) for n = 0..70</a>
%H A268851 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 A268851 a(n) ~ sqrt(8) * (8^8/7!)^n * n^(7*n) / exp(7*(n+1)). - _Vaclav Kotesovec_, Mar 03 2016
%t A268851 Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[k!/(i1!*i2!*i3!*i4!*i5!*i6!*i7!*(k - i1 - i2 - i3 - i4 - i5 - i6 - i7)!)*(8*k)!/(i1 + 2*i2 + 3*i3 + 4*i4 + 5*i5 + 6*i6 + 7*i7 + 8*(k - i1 - i2 - i3 - i4 - i5 - i6 - i7))!*(-1)^(i1 + 2*i2 + 3*i3 + 4*i4 + 5*i5 + 6*i6 + 7*i7 + 8*(k - i1 - i2 - i3 - i4 - i5 - i6 - i7) - k)/(5040^i1 * 720^i2 * 120^i3 * 24^i4 * 6^i5 * 2^i6), {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 A268851 Row n=8 of A047909.
%K A268851 nonn
%O A268851 0,3
%A A268851 _Alois P. Heinz_, Feb 14 2016