A214085 n^2 * (n^4 - n^2 + n + 1) / 2.

0, 1, 30, 342, 1960, 7575, 22806, 57820, 129312, 262845, 495550, 879186, 1483560, 2400307, 3747030, 5671800, 8358016, 12029625, 16956702, 23461390, 31924200, 42790671, 56578390, 73884372, 95392800, 121883125, 154238526, 193454730, 240649192, 297070635

Offset: 0

Author

Reinhard Zumkeller, Jul 07 2012

Keywords

• nonn
• easy

Comments

Row sums of the triangle in A214084.

Links

• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Programs

Haskell

a214085 n = n^2 * (n^4 - n^2 + n + 1) `div` 2

Magma

[n^2*(n^4-n^2+n+1)/2: n in [0..29]]; // Bruno Berselli, Jul 09 2012

Mathematica

Table[n^2 (n^4 - n^2 + n + 1)/2, {n, 0, 29}] (* Bruno Berselli, Jul 09 2012 *)
LinearRecurrence[{7,-21,35,-35,21,-7,1},{0,1,30,342,1960,7575,22806},40] (* Harvey P. Dale, Dec 12 2012 *)

Formula

a(n) = n * A000217(n) * A100104(n).

a(n) = A000217(A000578(n)) - A000217(A000290(n) - 1).

G.f.: x*(1+23*x+153*x^2+161*x^3+22*x^4)/(1-x)^7. - Bruno Berselli, Jul 09 2012

a(0)=0, a(1)=1, a(2)=30, a(3)=342, a(4)=1960, a(5)=7575, a(6)=22806, 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, Dec 12 2012