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

%I #12 Sep 08 2022 08:46:02

%S 0,1,30,342,1960,7575,22806,57820,129312,262845,495550,879186,1483560,

%T 2400307,3747030,5671800,8358016,12029625,16956702,23461390,31924200,

%U 42790671,56578390,73884372,95392800,121883125,154238526,193454730,240649192,297070635

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

%C Row sums of the triangle in A214084.

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).

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

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

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

%F 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

%t Table[n^2 (n^4 - n^2 + n + 1)/2, {n, 0, 29}] (* _Bruno Berselli_, Jul 09 2012 *)

%t LinearRecurrence[{7,-21,35,-35,21,-7,1},{0,1,30,342,1960,7575,22806},40] (* _Harvey P. Dale_, Dec 12 2012 *)

%o (Haskell)

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

%o (Magma) [n^2*(n^4-n^2+n+1)/2: n in [0..29]]; // _Bruno Berselli_, Jul 09 2012

%K nonn,easy

%O 0,3

%A _Reinhard Zumkeller_, Jul 07 2012