A244882 Expansion of (1 + 2*x + 2*x^2) / (1 - x)^6.

1, 8, 35, 110, 280, 616, 1218, 2220, 3795, 6160, 9581, 14378, 20930, 29680, 41140, 55896, 74613, 98040, 127015, 162470, 205436, 257048, 318550, 391300, 476775, 576576, 692433, 826210, 979910, 1155680, 1355816, 1582768, 1839145, 2127720, 2451435, 2813406

Offset: 0

Author

N. J. A. Sloane, Jul 08 2014

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• R. P. Stanley, Examples of Magic Labelings, Unpublished Notes, 1973 [Cached copy, with permission]See page 33.
• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Programs

Mathematica

CoefficientList[Series[(1+2x+2x^2)/(1-x)^6,{x,0,40}],x] (* or *) LinearRecurrence[{6,-15,20,-15,6,-1},{1,8,35,110,280,616},40] (* Harvey P. Dale, Dec 26 2016 *)

PARI

Vec((1 + 2*x + 2*x^2) / (1 - x)^6 + O(x^40)) \\ Colin Barker, Jan 12 2017

Formula

G.f.: (1 + 2*x + 2*x^2) / (1 - x)^6.

From Colin Barker, Jan 12 2017: (Start)

a(n) = (24 + 62*n + 63*n^2 + 33*n^3 + 9*n^4 + n^5) / 24.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>5.

(End)