A020548 3rd Euler polynomial evaluated at x=n! (multiplied by 4).

-1, -1, 9, 649, 51841, 6825601, 1489881601, 511943846401, 262183528857601, 191138113268121601, 191138824350351360001, 254405870811372994560001, 439613359905259699568640001, 965830554503712299093852160001, 2650239042150990796324586127360001, 8944556767403234966824310931456000001

Offset

0,3

Links

Table of n, a(n) for n=0..15.

Formula

a(n) = 4*(n!)^3 - 6*(n!)^2 + 1. - Christian Krause, Jun 08 2026

Prog

(PARI) a(n) = 4*eulerpol(3, n!) \\ Christian Krause, Jun 08 2026

Crossrefs

Sequence in context: A323425 A191510 A081232 * A091062 A221133 A015007

Adjacent sequences: A020545 A020546 A020547 * A020549 A020550 A020551

Keyword

sign,changed

Author

Simon Plouffe

Extensions

a(14)-a(15) from Christian Krause, Jun 08 2026

Status

approved