OFFSET
1,4
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. IV. Queens, Bishops, Nightriders (and Rooks), arXiv preprint arXiv:1609.00853 [math.CO], 2016-2020.
Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).
FORMULA
a(n) = 4! * binomial(n, 4)^2.
From Colin Barker, Jan 08 2013: (Start)
a(n) = (n^2*(-6+11*n-6*n^2+n^3)^2)/24.
G.f.: -24*x^4*(x^4 +16*x^3 +36*x^2 +16*x +1) / (x -1)^9.
(End)
From Amiram Eldar, Nov 02 2021: (Start)
Sum_{n>=4} 1/a(n) = (20*Pi^2 - 197)/9.
Sum_{n>=4} (-1)^n/a(n) = (64*log(2) - 44)/9. (End)
MATHEMATICA
LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {0, 0, 0, 24, 600, 5400, 29400, 117600, 381024}, 40] (* Harvey P. Dale, Feb 19 2013 *)
a[n_] := If[n<4, 0, Coefficient[n!*LaguerreL[n, x], x, n-4] // Abs];
Array[a, 30] (* Jean-François Alcover, Jun 14 2018, after A144084 *)
PROG
(PARI) a(n) = 4! * binomial(n, 4)^2; \\ Andrew Howroyd, Feb 13 2018
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Thomas Zaslavsky, Jun 27 2010
STATUS
approved