A145130 2 + (89040 + (71868 + (29932 + (8449 + (1960 + (322 + (28 + n)*n)*n)*n)*n)*n)*n)*n/40320.

2, 7, 25, 81, 236, 622, 1498, 3334, 6931, 13586, 25312, 45124, 77403, 128351, 206551, 323647, 495160, 741457, 1088891, 1571131, 2230702, 3120756, 4307096, 5870476, 7909201, 10542052, 13911562, 18187670, 23571781, 30301261, 38654397, 48955853, 61582654

Offset: 0

Author

Alois P. Heinz, Oct 03 2008

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (9, -36, 84, -126, 126, -84, 36, -9, 1).

Crossrefs

9th row of A145153. See row 9 of A145140/A145141 for rational coefficients and A145142 for 40320 * coefficients of polynomial.

Programs

Maple

a:= n-> 2+ (89040+ (71868+ (29932+ (8449+ (1960+ (322+ (28+ n) *n) *n) *n) *n) *n) *n) *n/40320: seq (a(n), n=0..40);

Mathematica

Table[2+(89040+(71868+(29932+(8449+(1960+(322+(28+n)n)n)n)n)n)n)n/40320,{n,0,40}] (* or *) LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{2,7,25,81,236,622,1498,3334,6931},40](* Harvey P. Dale, Dec 25 2011 *)
CoefficientList[Series[(x^8 - 8 x^7 + 28 x^6 - 56 x^5 + 71 x^4 - 60 x^3 + 34 x^2 - 11 x + 2) / (1 - x)^9, {x, 0, 50}], x] (* Vincenzo Librandi, Jun 06 2013 *)

PARI

a(n)=2+(89040+(71868+(29932+(8449+(1960+(322+(28+n)*n)*n)*n)*n)*n)*n)*n/40320 \\ Charles R Greathouse IV, Oct 07 2015

Formula

G.f.: (x^8-8*x^7+28*x^6-56*x^5+71*x^4-60*x^3+34*x^2-11*x+2) / (1-x)^9.

a(0)=2, a(1)=7, a(2)=25, a(3)=81, a(4)=236, a(5)=622, a(6)=1498, a(7)=3334, a(8)=6931, a(n)=9*a(n-1)-36*a(n-2)+84*a(n-3) -126*a(n-4) +126*a(n-5) -84*a(n-6) +36*a(n-7) -9*a(n-8) +a(n-9). - Harvey P. Dale, Dec 25 2011