A059600 Expansion of (1+6*x+x^2)/(1-x)^8.

1, 14, 85, 344, 1086, 2892, 6798, 14520, 28743, 53482, 94523, 159952, 260780, 411672, 631788, 945744, 1384701, 1987590, 2802481, 3888104, 5315530, 7170020, 9553050, 12584520, 16405155, 21179106, 27096759

Offset: 0

Author

Wolfdieter Lang, Feb 02 2001

Keywords

• nonn
• easy

Comments

a(n)= A038164(2*n).

Links

• Index entries for linear recurrences with constant coefficients, signature (8, -28, 56, -70, 56, -28, 8, -1).

Programs

Mathematica

CoefficientList[Series[(1+6x+x^2)/(1-x)^8,{x,0,30}],x] (* or *) LinearRecurrence[ {8,-28,56,-70,56,-28,8,-1},{1,14,85,344,1086,2892,6798,14520},30] (* Harvey P. Dale, Aug 18 2024 *)

Formula

a(n)= binomial(n+5, 5)*(4*n^2+24*n+21)/21.

G.f.: (1+6*x+x^2)/(1-x)^8.