cp's OEIS Frontend

A260727 Number of ways to place 3n rooks on an n X n board, with 3 rooks in each row and each column, multiple rooks in a cell allowed, and exactly 3 rooks below the main diagonal.

%I A260727 #31 Feb 22 2020 20:00:45
%S A260727 1,23,325,3368,28819,218788,1539399,10314315,66953292,425761614,
%T A260727 2671506918,16618186770,102796975770,633596982417,3896224129259,
%U A260727 23924104985984,146764696175937,899809941054468,5514653407814317,33789681789605283,207007665004469906
%N A260727 Number of ways to place 3n rooks on an n X n board, with 3 rooks in each row and each column, multiple rooks in a cell allowed, and exactly 3 rooks below the main diagonal.
%C A260727 a(n) is the number of minimal multiplex juggling patterns of period n using exactly 3 balls when we can catch/throw up to 3 balls at a time. (Minimal in the sense that each of the n throws is between 0 and n-1, inclusive.)
%H A260727 Colin Barker, <a href="/A260727/b260727.txt">Table of n, a(n) for n = 2..1000</a>
%H A260727 E. Banaian, S. Butler, C. Cox, J. Davis, J. Landgraf and S. Ponce, <a href="http://arxiv.org/abs/1508.03673">A generalization of Eulerian numbers via rook placements</a>, arXiv:1508.03673 [math.CO], 2015.
%F A260727 G.f.: -(700*x^13 - 2435*x^12 + 4558*x^11 - 7532*x^10 + 10404*x^9 - 9697*x^8 + 5545*x^7 - 1844*x^6 + 336*x^5 - 39*x^4 + 7*x^3 - x^2)/(4000*x^14 - 35400*x^13 + 143100*x^12 - 349910*x^11 + 577675*x^10 - 680496*x^9 + 589248*x^8 - 380592*x^7 + 184037*x^6 - 66214*x^5 + 17423*x^4 - 3246*x^3 + 404*x^2 - 30*x + 1).
%t A260727 CoefficientList[Series[-(700*x^13 - 2435*x^12 + 4558*x^11 - 7532*x^10 + 10404*x^9 - 9697*x^8 + 5545*x^7 - 1844*x^6 + 336*x^5 - 39*x^4 + 7*x^3 - x^2)/((x^2)*(4000*x^14 - 35400*x^13 + 143100*x^12 - 349910*x^11 + 577675*x^10 - 680496*x^9 + 589248*x^8 - 380592*x^7 + 184037*x^6 - 66214*x^5 + 17423*x^4 - 3246*x^3 + 404*x^2 - 30*x + 1)), {x, 0, 20}], x] (* _Wesley Ivan Hurt_, Jul 30 2015 *)
%Y A260727 Column k=3 of A269743.
%Y A260727 Cf. A260575, A260582, A260583, A260584, A260585.
%K A260727 nonn,easy
%O A260727 2,2
%A A260727 _Chris Cox_, Jul 30 2015