OFFSET
1,5
COMMENTS
Coefficient of q^3 in the polynomial NT_{n,mu}(q).
LINKS
M. Jones, S. Kitaev, J. Remmel, Frame patterns in n-cycles, arXiv preprint arXiv:1311.3332 [math.CO], 2013.
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
FORMULA
From Colin Barker, Jan 16 2014: (Start)
a(n) = (720-2136*n+2450*n^2-1395*n^3+425*n^4-69*n^5+5*n^6)/720.
G.f.: -x^4*(x^3+3*x^2+1) / (x-1)^7.
(End)
E.g.f.: (1/720)*exp(x)*x^3*(120 + 90*x + 36*x^2 + 5*x^3). - Stefano Spezia, Jan 09 2019
MAPLE
b:=binomial;
f:=n->b(n-1, 3)+3*b(n-1, 4)+6*b(n-1, 5)+5*b(n-1, 6);
[seq(f(n), n=1..50)];
MATHEMATICA
a[n_] := 1/720 (n-1)(n-2)(n-3)(-120 + 136n - 39n^2 + 5n^3); Array[a, 42] (* Jean-François Alcover, Jan 09 2019 *)
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 0, 0, 1, 7, 31, 106}, 50] (* Harvey P. Dale, Jul 27 2022 *)
PROG
(PARI) Vec(-x^4*(x^3+3*x^2+1)/(x-1)^7 + O(x^100)) \\ Colin Barker, Jan 16 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jan 13 2014
STATUS
approved