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 A121563 #16 Oct 21 2024 12:59:43
%S A121563 0,1,3,31,523,333787,3029083,357534985867,1466339436008107,
%T A121563 86629054728081110243,54153614078975016066611,
%U A121563 1404709830784309760237846406097211,1404749977001540310126014452972211
%N A121563 Numerator of Sum_{i=1..n} i!/(i^i).
%F A121563 Numerator of Sum_{i=1..n} A000142(i)/A000312(i).
%F A121563 Limit_{n -> oo} A121563(n)/A121564(n) = A094082.
%e A121563 A121563/A121564 = 0, 1, 3/2, 31/18, 523/288, 333787/180000, ... .
%t A121563 Numerator[Table[Sum[i!/(i^i),{i,n}],{n,12}]] (* _James C. McMahon_, Oct 19 2024 *)
%Y A121563 Denominators are in A121564.
%Y A121563 Cf. A000142, A000312, A055775, A094082.
%K A121563 easy,frac,nonn
%O A121563 0,3
%A A121563 _Jonathan Vos Post_, Aug 07 2006