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 A309483 #11 Aug 04 2019 20:04:00
%S A309483 1,1,4,96,356540,39903286,1312583081304,356826497344324,
%T A309483 51202108292508282304,10903333036235662560405182340,
%U A309483 8851961858819132893480466080328,10341369256681418109100257759613689061054,20410983764150196478167108200311379711212644128
%N A309483 Quotients (!p - Bell(p-1) + 1)/p where p is the n-th prime, !k is Kurepa's left-factorial function (A003422) and Bell(k) is the k-th Bell number (A000110).
%C A309483 Gertsch Hamadene proved that !p == Bell(p-1) - 1 (mod p) for primes p.
%H A309483 Daniel Barsky and Bénali Benzaghou, <a href="http://www.numdam.org/item/JTNB_2004__16_1_1_0/">Nombres de Bell et somme de factorielles</a>, Journal de théorie des nombres de Bordeaux, Vol. 16, No. 1 (2004), pp. 1-17.
%H A309483 Anne Gertsch Hamadene, <a href="http://doc.rero.ch/record/4372/files/2_these_GertschHamadeneA.pdf">Congruences pour quelques suites classiques de nombres, sommes de factorielles et calcul ombral</a>, Doctoral dissertation, Université de Neuchâtel, 1999.
%e A309483 The 3rd prime is 5, so a(3) = (!5 - Bell(5-1) + 1)/5 = (34 - 15 + 1)/5 = 4.
%t A309483 quot[p_] := (Sum[k!, {k, 0, p - 1}] - BellB[p - 1] + 1)/p; Table[quot[Prime[i]], {i, 1, 13}]
%o A309483 (PARI) a(n) = my(p=prime(n)); (a003422(p) - a000110(p-1) + 1)/p \\ _Felix Fröhlich_, Aug 04 2019
%Y A309483 Cf. A000110, A003422, A079609.
%K A309483 nonn
%O A309483 1,3
%A A309483 _Amiram Eldar_, Aug 04 2019