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A256467
Inverse Lah transform of the squares.
1
0, 1, 2, -9, 28, -55, -234, 5047, -59464, 620433, -6210710, 60312791, -552386988, 4291343641, -14786103682, -469083221865, 17904311480176, -458594711604703, 10473023418660306, -228670491372982217, 4899169866194557580, -104056906653521654679, 2196053393686810460902
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
Cf. A103194.
Sequence in context: A100293 A202679 A340049 * A303373 A001093 A248658
KEYWORD
sign
AUTHOR
Peter Luschny, Mar 30 2015
STATUS
approved