OFFSET
0,3
COMMENTS
The row polynomials of the rencontres numbers (A008290) evaluated at -1/2 and normalized by (-2)^n.
FORMULA
a(n) = (-2)^n*Sum_{k=0..n} binomial(n, k)*subfactorial(n - k)*(-1/2)^k.
a(n) = 6*(n - 1)*a(n - 2) - (2*n - 3)*a(n - 1) for n >= 3.
MAPLE
egf := exp(-3*x)/(1 - 2*x): ser := series(egf, x, 32):
seq((-1)^n*n!*coeff(ser, x, n), n=0..20);
MATHEMATICA
a[n_] := (-2)^n Sum[Binomial[n, k] Subfactorial[n - k] (-2)^(-k), {k, 0, n}];
Table[a[n], {n, 0, 20}]
PROG
CROSSREFS
KEYWORD
sign
AUTHOR
Peter Luschny, Apr 24 2021
STATUS
approved