A168351 a(n) = n^5*(n+1)/2.

0, 1, 48, 486, 2560, 9375, 27216, 67228, 147456, 295245, 550000, 966306, 1617408, 2599051, 4033680, 6075000, 8912896, 12778713, 17950896, 24760990, 33600000, 44925111, 59266768, 77236116, 99532800, 126953125, 160398576, 200884698

Offset: 0

Author

N. J. A. Sloane, Dec 11 2009

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, 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).

Crossrefs

Sequences of the form n^5*(n^k + 1)/2: A000584 (k=0), this sequence (k=1), A168364 (k=2), A168371 (k=3), A168372 (k=4), A071236 (k=5), A168412 (k=6), A168432 (k=7), A168462 (k=8), A168471 (k=9), A168507 (k=10).

Programs

Magma

[n^5*(n+1)/2: n in [0..30]]; // Vincenzo Librandi, Aug 28 2011

Mathematica

Table[n^5*(n + 1)/2, {n, 0, 40}] (* Wesley Ivan Hurt, Aug 13 2015 *)

SageMath

def A168351(n): return n^4*binomial(n+1,2)
print([A168351(n) for n in range(41)]) # G. C. Greubel, Mar 20 2025

Formula

a(n) = Sum_{i=1..n} Sum_{j=1..n} Sum_{k=1..n} Sum_{l=1..n} Sum_{m=1..n} (i+j+k-l-m). - Wesley Ivan Hurt, Aug 13 2015

From G. C. Greubel, Mar 20 2025: (Start)

G.f.: x*(1 + 41*x + 171*x^2 + 131*x^3 + 16*x^4)/(1-x)^7.

E.g.f.: (1/2)*x*(2 + 46*x + 115*x^2 + 75*x^3 + 16*x^4 + x^5)*exp(x). (End)