A294193 a(n) = sum of integers between n!+1 and (n+1)!.

0, 2, 18, 279, 6960, 252300, 12443760, 800168040, 65028257280, 6518255405760, 790091384544000, 113924591159702400, 19273172758289049600, 3780639334294658035200, 851206099134433961318400, 218026562222345234117760000, 63037891684425054948655104000

Offset: 0

Author

Olivier Gérard, Oct 24 2017

Keywords

• nonn
• easy

Comments

Useful as a growth reference for sequences summing on intervals between 2 factorials.

Examples

			a(2) = 3 + 4 + 5 + 6 = 18.
a(3) = 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 + 21 + 22 + 23 + 24 = 24*25/2 - 6*7/2 = 279.
		

Links

• Iain Fox, Table of n, a(n) for n = 0..252

Crossrefs

Cf. A000217 (triangular numbers).

Cf. A001563 (difference of factorials).

Cf. A049775 (same idea between consecutive powers of 2).

Cf. A000142, A055555.

Programs

Mathematica

Table[1/2 ((n + 1)! ((n + 1)! + 1) - n! (n! + 1) ), {n, 0, 10}]

PARI

a(n) = 1/2*((n+1)!*((n+1)! + 1)-n!*(n!+1)) \\ Iain Fox, Nov 28 2017

Formula

a(n) = (1/2) * ((n + 1)!*((n + 1)! + 1) - n!*(n! + 1) ).

a(n) = A055555(n+1) - A055555(n). - J.S. Seneschal, Jul 07 2025

Extensions

More terms from Iain Fox, Nov 28 2017