A256467 Inverse Lah transform of the squares.

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

Links

Table of n, a(n) for n=0..22.

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

Adjacent sequences: A256464 A256465 A256466 * A256468 A256469 A256470

Keyword

sign

Author

Peter Luschny, Mar 30 2015

Status

approved