%I #27 Sep 08 2022 08:46:09

%S 0,0,59,1040,7014,29580,94105,247884,570220,1184424,2271735,4087160,

%T 6977234,11399700,17945109,27360340,40574040,58723984,83186355,

%U 115606944,157934270,212454620,281829009,369132060,477892804,612137400,776433775,975938184,1216443690

%N (16n^6 - 24n^5 + 2n^4 + 11n^3 - 6n^2 + n) / 6.

%C For n > 0: a(n) = A245826(2*n-1,n), central terms of triangle A245826.

%H Reinhard Zumkeller, <a href="/A245941/b245941.txt">Table of n, a(n) for n = 0..10000</a>

%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 G.f.: -x^2*(4*x^4+257*x^3+973*x^2+627*x+59) / (x-1)^7. - _Colin Barker_, Aug 08 2014

%F a(n) = (n-1)*n*(2*n-1)*(8*n^3-3*n+1)/6. [_Bruno Berselli_, Aug 08 2014]

%F a(0)=0, a(1)=0, a(2)=59, a(3)=1040, a(4)=7014, a(5)=29580, a(6)=94105, 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 13 2015

%p A245941:=n->(16*n^6-24*n^5+2*n^4+11*n^3-6*n^2+n)/6: seq(A245941(n), n=0..30); # _Wesley Ivan Hurt_, Aug 09 2014

%t Table[(16 n^6 - 24 n^5 + 2 n^4 + 11 n^3 - 6 n^2 + n)/6, {n, 0, 30}] (* _Vincenzo Librandi_, Aug 09 2014 *)

%t LinearRecurrence[{7,-21,35,-35,21,-7,1},{0,0,59,1040,7014,29580,94105},30] (* _Harvey P. Dale_, Apr 13 2015 *)

%o (Haskell)

%o a245941 n = n * (16*n^5 - 24*n^4 + 2*n^3 + 11*n^2 - 6*n + 1) `div` 6

%o (PARI)

%o concat([0,0], Vec(-x^2*(4*x^4+257*x^3+973*x^2+627*x+59)/(x-1)^7 + O(x^100))) \\ _Colin Barker_, Aug 08 2014

%o (Magma) [(16*n^6-24*n^5+2*n^4+11*n^3-6*n^2+n)/6: n in [0..30]] // _Vincenzo Librandi_, Aug 09 2014

%K nonn,easy

%O 0,3

%A _Reinhard Zumkeller_, Aug 07 2014