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 A363697 #17 Jul 03 2023 00:53:10
%S A363697 1,3,19,47,601,2039,35281,-26881,4898881,-8104321,439084801,576132479,
%T A363697 80951270401,-913158005761,49506372115201,-558073906790401,
%U A363697 6046686277632001,79958674981785599,2311256907767808001,-115583806104986419201
%N A363697 a(n) = -n! * Sum_{d|n} (-n/d)^d / d!.
%H A363697 Seiichi Manyama, <a href="/A363697/b363697.txt">Table of n, a(n) for n = 1..447</a>
%F A363697 E.g.f.: Sum_{k>0} (1 - exp(-k * x^k)).
%F A363697 If p is prime, a(p) = (-1)^(p+1) + p * p!.
%t A363697 a[n_] := -n! * DivisorSum[n, (-n/#)^#/#! &]; Array[a, 20] (* _Amiram Eldar_, Jul 03 2023 *)
%o A363697 (PARI) a(n) = -n!*sumdiv(n, d, (-n/d)^d/d!);
%Y A363697 Cf. A132958, A363698.
%Y A363697 Cf. A354843.
%K A363697 sign,easy
%O A363697 1,2
%A A363697 _Seiichi Manyama_, Jun 16 2023