OFFSET
0,5
COMMENTS
The polynomials generate (-1)^k*n! times the diagonals of A098493.
LINKS
Seiichi Manyama, Rows n = 0..139, flattened
Alex Fink, Richard K. Guy, and Mark Krusemeyer, Partitions with parts occurring at most thrice, Contributions to Discrete Mathematics, Vol 3, No 2 (2008), pp. 76-114.
FORMULA
E(n+1,x+1) - E(n+1,x) = (n+1) * ( E(n,x) - n * E(n-1,x-1) ).
EXAMPLE
E(0,x) = 1
E(1,x) = x - 1
E(2,x) = x^2 - 5*x + 4
E(3,x) = x^3 - 12*x^2 + 35*x - 30
E(4,x) = x^4 - 22*x^3 + 143*x^2 - 362*x + 312
E(5,x) = x^5 - 35*x^4 + 405*x^3 - 2065*x^2 + 4814*x - 4200
CROSSREFS
Columns include -A000326.
Row sums are E(n, 1) = (-1)^n*n!*A005774(n-2). [corrected by Seiichi Manyama, Feb 04 2023]
KEYWORD
sign,tabl
AUTHOR
Ralf Stephan, Sep 12 2004
STATUS
approved