A168122 n^2*(n^4+1)/2.

0, 1, 34, 369, 2056, 7825, 23346, 58849, 131104, 265761, 500050, 885841, 1493064, 2413489, 3764866, 5695425, 8388736, 12068929, 17006274, 23523121, 32000200, 42883281, 56690194, 74018209, 95551776, 122070625, 154458226, 193710609

Offset: 0

Author

N. J. A. Sloane, Dec 11 2009

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (7, -21, 35, -35, 21, -7, 1).

Programs

Mathematica

Table[n^2 (n^4+1)/2, {n, 0, 30}] (* or *) LinearRecurrence[ {7, -21, 35, -35, 21, -7, 1}, {0, 1, 34, 369, 2056, 7825, 23346}, 30] (* Harvey P. Dale, Apr 21 2014 *)
CoefficientList[Series[x (1 + x) (1 + 26 x + 126 x^2 + 26 x^3 + x^4)/(1 - x)^7, {x, 0, 40}], x] (* Vincenzo Librandi, Apr 23 2014 *)

Formula

a(0)=0, a(1)=1, a(2)=34, a(3)=369, a(4)=2056, a(5)=7825, a(6)=23346; for n>6, 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). - Harvey P. Dale, Apr 21 2014

G.f.: x*(1 + x)*(1 + 26*x + 126*x^2 + 26*x^3 + x^4)/(1-x)^7. - Vincenzo Librandi, Apr 23 2014