A179062 Number of non-attacking placements of 7 rooks on an n X n board.

0, 0, 0, 0, 0, 0, 5040, 322560, 6531840, 72576000, 548856000, 3161410560, 14841066240, 59364264960, 208702494000, 659602944000, 1906252508160, 5104345559040, 12796310741760, 30287126016000, 68146033536000, 146589689917440, 302913851430960, 603731413232640

Offset

1,7

Links

Andrew Howroyd, Table of n, a(n) for n = 1..200

Seth Chaiken, Christopher R. H. Hanusa, and Thomas Zaslavsky, A q-Queens Problem. V. Some of Our Favorite Pieces: Queens, Bishops, Rooks, and Nightriders, arXiv:1609.00853 [math.CO], 2016-2020.

Index entries for linear recurrences with constant coefficients, signature (15,-105,455,-1365,3003,-5005,6435,-6435,5005,-3003,1365,-455,105,-15,1).

Formula

a(n) = 7!*binomial(n,7)^2.

G.f.: -5040*x^7*(x+1)*(x^6+48*x^5+393*x^4+832*x^3+393*x^2+48*x+1) / (x-1)^15. - Colin Barker, Jan 08 2013

From Amiram Eldar, Sep 27 2025: (Start)

Sum_{n>=7} 1/a(n) = 539*Pi^2/360 - 6383573/432000.

Sum_{n>=7} (-1)^(n+1)/a(n) = 41503/259200 - 7*Pi^2/432. (End)

Mathematica

7! Binomial[Range[30], 7]^2 (* or *) LinearRecurrence[{15, -105, 455, -1365, 3003, -5005, 6435, -6435, 5005, -3003, 1365, -455, 105, -15, 1}, {0, 0, 0, 0, 0, 0, 5040, 322560, 6531840, 72576000, 548856000, 3161410560, 14841066240, 59364264960, 208702494000}, 30] (* Harvey P. Dale, May 25 2017 *)

Prog

(PARI) a(n) = 7! * binomial(n, 7)^2 \\ Andrew Howroyd, Feb 13 2018

Crossrefs

Column k=7 of A144084.

Cf. A179061 (6 rooks), A179063 (8 rooks).

Sequence in context: A228910 A258419 A355023 * A342075 A055362 A246195

Adjacent sequences: A179059 A179060 A179061 * A179063 A179064 A179065

Keyword

easy,nonn

Author

Thomas Zaslavsky, Jun 27 2010

Status

approved