A260583 Number of ways to place 3n rooks on an n X n board, 3 rooks in each row and each column, multiple rooks in an allowed cell, and exactly 4 rooks below the main diagonal.
11, 595, 14679, 253247, 3564803, 44226950, 505572550, 5473391465, 57122380066, 581477852342, 5819301681925, 57564437594318, 564911137682637, 5513703983635512, 53616132982114742, 520057429817203110, 5035740328012627416, 48704838658567681135
Offset: 3
Keywords
Links
- Colin Barker, Table of n, a(n) for n = 3..1000
- E. Banaian, S. Butler, C. Cox, J. Davis, J. Landgraf and S. Ponce A generalization of Eulerian numbers via rook placements, arXiv:1508.03673 [math.CO], 2015.
Formula
G.f.: -(24558000*x^24 - 221169800*x^23 + 1030045255*x^22 - 3270869391*x^21 + 7705144467*x^20 - 13843184523*x^19 + 19209151138*x^18 - 20800159606*x^17 + 17768204859*x^16 - 12126221923*x^15 + 6718636422*x^14 - 3086566305*x^13 + 1204914514*x^12 - 407103232*x^11 + 118646908*x^10 - 28836372*x^9 + 5505383*x^8 - 758705*x^7 + 65305*x^6 - 2162*x^5 - 131*x^4 + 11*x^3)/(133600000*x^25 - 1875920000*x^24 + 12500686000*x^23 - 52604444000*x^22 + 156920670600*x^21 - 353103818000*x^20 + 622718972395*x^19 - 882777307660*x^18 + 1023713051333*x^17 - 983132187597*x^16 + 788634518440*x^15 - 531447118763*x^14 + 301890662895*x^13 - 144761728498*x^12 + 58568440406*x^11 - 19945788669*x^10 + 5692551701*x^9 - 1352405718*x^8 + 264899104*x^7 - 42210805*x^6 + 5370925*x^5 - 531418*x^4 + 39303*x^3 - 2039*x^2 + 66*x - 1).
Comments