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 A055555 #34 Apr 02 2025 18:03:44
%S A055555 1,1,3,21,300,7260,259560,12703320,812871360,65841128640,
%T A055555 6584096534400,796675481078400,114721266640780800,
%U A055555 19387894024929830400,3800027228319587865600,855006126362753549184000,218881568348707987666944000,63256773252773762936322048000
%N A055555 a(n) = n!*(n!+1)/2.
%C A055555 a(n) is the number of unordered pairs (not necessarily distinct) of elements in S_n (the symmetric group on n letters). That is, a(n) = binomial(n!,2) + n!. - _Geoffrey Critzer_, Jan 09 2016
%F A055555 a(n) + (-n^2-n-3)*a(n-1) + (n-1)*(n^2+2*n-1)*a(n-2) - 2*(n-1)*(n-2)^2*a(n-3) = 0. - _R. J. Mathar_, Mar 21 2013
%F A055555 a(n) = Sum_{k=1..n!} k. - _Pedro Caceres_, Mar 10 2018
%F A055555 a(n) = A000217(A000142(n)). - _Michel Marcus_, Mar 11 2018
%t A055555 Table[n!*(n! + 1)/2, {n, 0, 20}] (* _Vladimir Joseph Stephan Orlovsky_, Jul 07 2011 *)
%o A055555 (Magma) [Factorial(n)*(Factorial(n)+1)/2: n in [0..20]]; // _Vincenzo Librandi_, Jan 10 2016
%o A055555 (PARI) a(n) = n!*(n!+1)/2; \\ _Altug Alkan_, Jan 10 2015
%o A055555 (Sage) [factorial(n)*(factorial(n)+1)/2 for n in range(0,18)] # _Stefano Spezia_, Apr 02 2025
%Y A055555 Cf. A000142, A000217.
%K A055555 nonn
%O A055555 0,3
%A A055555 _N. J. A. Sloane_, Jul 19 2000