A235593 Binomial(n-1,3)+3*binomial(n-1,4)+6*binomial(n-1,5)+5*binomial(n-1,6).

0, 0, 0, 1, 7, 31, 106, 301, 742, 1638, 3312, 6237, 11077, 18733, 30394, 47593, 72268, 106828, 154224, 218025, 302499, 412699, 554554, 734965, 961906, 1244530, 1593280, 2020005, 2538081, 3162537, 3910186, 4799761, 5852056, 7090072, 8539168, 10227217, 12184767, 14445207, 17044938, 20023549, 23423998, 27292798

Offset

1,5

Comments

Coefficient of q^3 in the polynomial NT_{n,mu}(q).

Links

Table of n, a(n) for n=1..42.

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

Cf. A235594.

Sequence in context: A222265 A107392 A054497 * A119359 A055366 A160607

Adjacent sequences: A235590 A235591 A235592 * A235594 A235595 A235596

Keyword

nonn,easy

Author

N. J. A. Sloane, Jan 13 2014

Status

approved