This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A294193 #18 Jul 07 2025 10:44:28
%S A294193 0,2,18,279,6960,252300,12443760,800168040,65028257280,6518255405760,
%T A294193 790091384544000,113924591159702400,19273172758289049600,
%U A294193 3780639334294658035200,851206099134433961318400,218026562222345234117760000,63037891684425054948655104000
%N A294193 a(n) = sum of integers between n!+1 and (n+1)!.
%C A294193 Useful as a growth reference for sequences summing on intervals between 2 factorials.
%H A294193 Iain Fox, <a href="/A294193/b294193.txt">Table of n, a(n) for n = 0..252</a>
%F A294193 a(n) = (1/2) * ((n + 1)!*((n + 1)! + 1) - n!*(n! + 1) ).
%F A294193 a(n) = A055555(n+1) - A055555(n). - _J.S. Seneschal_, Jul 07 2025
%e A294193 a(2) = 3 + 4 + 5 + 6 = 18.
%e A294193 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.
%t A294193 Table[1/2 ((n + 1)! ((n + 1)! + 1) - n! (n! + 1) ), {n, 0, 10}]
%o A294193 (PARI) a(n) = 1/2*((n+1)!*((n+1)! + 1)-n!*(n!+1)) \\ _Iain Fox_, Nov 28 2017
%Y A294193 Cf. A000217 (triangular numbers).
%Y A294193 Cf. A001563 (difference of factorials).
%Y A294193 Cf. A049775 (same idea between consecutive powers of 2).
%Y A294193 Cf. A000142, A055555.
%K A294193 nonn,easy
%O A294193 0,2
%A A294193 _Olivier Gérard_, Oct 24 2017
%E A294193 More terms from _Iain Fox_, Nov 28 2017