A245941 (16n^6 - 24n^5 + 2n^4 + 11n^3 - 6n^2 + n) / 6.

0, 0, 59, 1040, 7014, 29580, 94105, 247884, 570220, 1184424, 2271735, 4087160, 6977234, 11399700, 17945109, 27360340, 40574040, 58723984, 83186355, 115606944, 157934270, 212454620, 281829009, 369132060, 477892804, 612137400, 776433775, 975938184, 1216443690

Offset: 0

Author

Reinhard Zumkeller, Aug 07 2014

Keywords

• nonn
• easy

Comments

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

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Programs

Haskell

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

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

Maple

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

Mathematica

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

PARI

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

Formula

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

a(n) = (n-1)*n*(2*n-1)*(8*n^3-3*n+1)/6. [Bruno Berselli, Aug 08 2014]

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