A047663 Row 6 of square array defined in A047662.

6, 42, 188, 644, 1826, 4494, 9912, 20040, 37758, 67122, 113652, 184652, 289562, 440342, 651888, 942480, 1334262, 1853754, 2532396, 3407124, 4520978, 5923742, 7672616, 9832920, 12478830, 15694146, 19573092, 24221148, 29755914, 36308006

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Muniru A Asiru, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (7, -21, 35, -35, 21, -7, 1).

Programs

GAP

List([1..35],n->n/45*(2*n^5+6*n^4+35*n^3+60*n^2+98*n+69)); # Muniru A Asiru, Nov 21 2018

Maple

seq(coeff(series(x*(-6*x^4-20*x^2-6)/(x-1)^7,x,n+1), x, n), n = 1 .. 35); # Muniru A Asiru, Nov 21 2018

Mathematica

LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {6, 42, 188, 644, 1826, 4494, 9912 }, 50] (* or *)
CoefficientList[Series[-((2 (3 + 10 x^2 + 3 x^4))/(-1 + x)^7), {x, 0, 50}], x] (* Stefano Spezia, Nov 01 2018 *)

Formula

a(n) = (n/45) * (2n^5 + 6n^4 + 35n^3 + 60n^2 + 98n + 69).

From Chai Wah Wu, Nov 01 2018: (Start)

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n > 7.

G.f.: x*(-6*x^4 - 20*x^2 - 6)/(x - 1)^7. (End)