A163274 a(n) = n^4*(n+1)^2/2.

0, 2, 72, 648, 3200, 11250, 31752, 76832, 165888, 328050, 605000, 1054152, 1752192, 2798978, 4321800, 6480000, 9469952, 13530402, 18948168, 26064200, 35280000, 47064402, 61960712, 80594208, 103680000, 132031250, 166567752, 208324872

Offset: 0

Author

Omar E. Pol, Jul 24 2009

Keywords

• easy
• nonn

Comments

Row sums of triangle A163284.

Links

• Harvey P. Dale, 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).

Crossrefs

Cf. A006002, A099903, A163102, A163275, A163276, A163277, A163284.

Programs

Mathematica

Table[(n^4 (n+1)^2)/2,{n,0,30}] (* or *) LinearRecurrence[ {7,-21,35,-35,21,-7,1},{0,2,72,648,3200,11250,31752},30] (* Harvey P. Dale, May 07 2012 *)

PARI

a(n)=n^4*(n+1)^2/2 \\ Charles R Greathouse IV, Oct 07 2015

Formula

From R. J. Mathar, Jul 29 2009: (Start)

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).

G.f.: -2*x*(1 + 29*x + 93*x^2 + 53*x^3 + 4*x^4)/(x-1)^7. (End)

From Amiram Eldar, May 14 2022: (Start)

Sum_{n>=1} 1/a(n) = 4*Pi^2/3 + Pi^4/45 - 4*zeta(3) - 10.

Sum_{n>=1} (-1)^(n+1)/a(n) = 10 + Pi^2/3 + 7*Pi^4/360 - 16*log(2) - 3*zeta(3). (End)

Extensions

More terms from R. J. Mathar, Jul 29 2009