A020547 2nd Euler polynomial x^2 - x evaluated at x=n!.

0, 0, 2, 30, 552, 14280, 517680, 25396560, 1625662080, 131681531520, 13168185811200, 1593350882323200, 229442532323558400, 38775788037405619200, 7600054456464819148800, 1710012252722891749632000, 437763136697374129754112000

Offset: 0

Author

Simon Plouffe

Keywords

• nonn
• easy

Links

• Eric Weisstein's World of Mathematics, Euler Polynomial.

Crossrefs

Cf. A000142 (n!), A055555.

Programs

Magma

[Factorial(n)*(Factorial(n)-1): n in [0..30]]; // Vincenzo Librandi, Apr 15 2015

Mathematica

Table[n! (n! - 1), {n, 0, 20}] (* Vincenzo Librandi, Apr 15 2015 *)

PARI

vector(20, n, n--; (n!)^2-n!) \\ Michel Marcus, Apr 15 2015

Formula

a(n) = n!*(n!-1). - Mark van Hoeij, May 13 2013

a(n) = A000142(n)*A000142(n-1). - Michel Marcus, Apr 15 2015

a(n) = 2*(A055555(n) - A000142(n)). - J.S. Seneschal, Jul 01 2025