OFFSET
0,3
FORMULA
a(n) = Sum_{k=0..n}(-1)^(n-k)*(n-k)!*C(n,n-k)*C(n-1,n-k)*k^2.
a(n) = (-1)^(n+1)*n!*hypergeom([2, 1-n], [1, 1], 1)) for n>=1.
D-finite with recurrence +(-n+1)*a(n) +(-2*n^2+3*n+4)*a(n-1) -(n-1)*(n-2)*(n+1)*a(n-2)=0. - R. J. Mathar, Jul 27 2022
MAPLE
a := n -> `if`(n=0, 0, -(-1)^n*n!*hypergeom([2, 1-n], [1, 1], 1)):
seq(simplify(a(n)), n=0..22);
CROSSREFS
KEYWORD
sign
AUTHOR
Peter Luschny, Mar 30 2015
STATUS
approved