A055555 a(n) = n!*(n!+1)/2.

1, 1, 3, 21, 300, 7260, 259560, 12703320, 812871360, 65841128640, 6584096534400, 796675481078400, 114721266640780800, 19387894024929830400, 3800027228319587865600, 855006126362753549184000, 218881568348707987666944000, 63256773252773762936322048000

Offset: 0

Author

N. J. A. Sloane, Jul 19 2000

Keywords

• nonn

Comments

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

Crossrefs

Cf. A000142, A000217.

Programs

Magma

[Factorial(n)*(Factorial(n)+1)/2: n in [0..20]]; // Vincenzo Librandi, Jan 10 2016

Mathematica

Table[n!*(n! + 1)/2, {n, 0, 20}] (* Vladimir Joseph Stephan Orlovsky, Jul 07 2011 *)

PARI

a(n) = n!*(n!+1)/2; \\ Altug Alkan, Jan 10 2015

Sage

[factorial(n)*(factorial(n)+1)/2 for n in range(0,18)] # Stefano Spezia, Apr 02 2025

Formula

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

a(n) = Sum_{k=1..n!} k. - Pedro Caceres, Mar 10 2018

a(n) = A000217(A000142(n)). - Michel Marcus, Mar 11 2018