A108495 a(n) = (n^7 - n)/6.

0, 0, 21, 364, 2730, 13020, 46655, 137256, 349524, 797160, 1666665, 3247860, 5971966, 10458084, 17568915, 28476560, 44739240, 68389776, 102036669, 148978620, 213333330, 300181420, 415726311, 567470904, 764411900, 1017252600

Offset: 0

Author

Henry Bottomley, Jun 06 2005

Keywords

• nonn
• easy

Comments

Also integer sequences for (n^2-n)/1 (A002378 offset), (n^3-n)/2 (A027480 offset), (n^43-n)/42 (A108496) and (n^1807-n)/1806.

Examples

			a(2) = (2^7 - 2)/6 = 126/6 = 21.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• D. Zagier, Problems posed at the St Andrews Colloquium, 1996.
• Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Crossrefs

Cf. A014117, A108497, A108499.

Programs

Magma

[(n^7-n)/6: n in [0..40]]; // Vincenzo Librandi, May 02 2011

Mathematica

Table[(n^7-n)/6,{n,0,30}] (* or *) LinearRecurrence[ {8,-28,56,-70,56,-28,8,-1},{0,0,21,364,2730,13020,46655,137256},30] (* Harvey P. Dale, Apr 16 2014 *)

Python

[(n**7-n)//6 for n in range(41)] # David Radcliffe, Jun 06 2025

Formula

a(n) = (n-1)*A059721(n) = -A024004(n)*n/6.

G.f.: 7*x^2*(3 + 28*x + 58*x^2 + 28*x^3 + 3*x^4)/(1-x)^8. [Colin Barker, May 08 2012]