A160837 G.f.: (1+38*x+262*x^2+475*x^3+254*x^4+37*x^5+x^6)/(1-x)^7.

1, 45, 556, 3457, 14317, 45565, 120772, 280001, 586225, 1132813, 2052084, 3524929, 5791501, 9162973, 14034364, 20898433, 30360641, 43155181, 60162076, 82425345, 111172237, 147833533, 194064916, 251769409, 323120881, 410588621, 516962980

Offset: 0

Author

N. J. A. Sloane, Nov 18 2009

Keywords

• nonn
• easy

Comments

Source: the De Loera et al. article and the Haws website listed in A160747.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Programs

Magma

[1+ n*(n+1)*(89*n^4+183*n^3+427*n^2+333*n+288)/60: n in [0..30]]; // Vincenzo Librandi, Sep 19 2011

Mathematica

CoefficientList[Series[(1+38x+262x^2+475x^3+254x^4+37x^5+x^6)/(1-x)^7, {x,0,40}], x] (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1},{1, 45, 556,3457,14317,45565,120772}, 40] (* Harvey P. Dale, Nov 27 2016 *)

PARI

x='x+O('x^30); Vec((1+38*x+262*x^2+475*x^3+254*x^4+37*x^5+x^6)/(1-x)^7) \\ G. C. Greubel, Apr 28 2018

Formula

From R. J. Mathar, Dec 16 2009: (Start)

a(n) = 1+24/5*n+38/3*n^3+207/20*n^2+61/6*n^4+68/15*n^5+89/60*n^6.

a(n) = 1+ n*(n+1)*(89*n^4+183*n^3+427*n^2+333*n+288)/60. (End)