A256467 - OEIS

%I #9 Nov 13 2024 22:43:21

%S 0,1,2,-9,28,-55,-234,5047,-59464,620433,-6210710,60312791,-552386988,

%T 4291343641,-14786103682,-469083221865,17904311480176,

%U -458594711604703,10473023418660306,-228670491372982217,4899169866194557580,-104056906653521654679,2196053393686810460902

%N Inverse Lah transform of the squares.

%F a(n) = Sum_{k=0..n}(-1)^(n-k)*(n-k)!*C(n,n-k)*C(n-1,n-k)*k^2.

%F a(n) = (-1)^(n+1)*n!*hypergeom([2, 1-n], [1, 1], 1) for n>=1.

%F 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

%p a := n -> `if`(n=0,0, -(-1)^n*n!*hypergeom([2, 1-n], [1, 1], 1)):

%p seq(simplify(a(n)), n=0..22);

%Y Cf. A103194.

%K sign

%O 0,3

%A _Peter Luschny_, Mar 30 2015