0,2

Also determinant of n X n matrix with m(i,j) = i^2 if i=j otherwise 1. - Robert G. Wilson v (rgwv(AT)rgwv.com), Jan 28 2002

Partial products of positive values of A005563. - Jonathan Vos Post (jvospost3(AT)gmail.com), Oct 21 2008

This sequence has been shown to contain infinitely many squares. From the Hong and Liu abstract: Recently Cilleruelo proved that the product Product[k=1..n](k^2 + 1) is a square only for n = 3 which confirms a conjecture of Amdeberhan, Medina and Moll. In this paper, we show that the sequence Product[k=2..n](k^2 - 1)} contains infinitely many squares. Furthermore, we determine all squares in this sequence. We also give a formula for the p-adic valuation of the terms in this sequence. - Jonathan Vos Post (jvospost3(AT)gmail.com), Oct 21 2008

Equals (-1)^n * (1, 1, 3, 24, 360,...) dot (1, -4, 9, -16, 25,...). [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 21 2009]

J. Cilleruelo, Squares in (1^2 + 1) . . . (n^2 + 1), J. Number Theory 128 (2008), 2488-2491.

Shaofang Hong, Xingjiang Liu, Squares in (2^2-1)...(n^2-1) and p-adic valuation, Oct 19, 2008.

Index entries for sequences related to factorial numbers

Example: a(4) = 8640 = (1, 1, 3, 24, 360) dot (1, -4, 9, -16, 25) = (1, -4, 27, -384, 9000). [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 21 2009]

f := n->n!*(n+2)!/2;

(Other) sage: [stirling_number1(n, 1)*factorial(n-3)/2 for n in xrange(3, 18)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 07 2009]

Sequence in context: A082166 A144003 A153389 this_sequence A145169 A065761 A002832

Adjacent sequences: A010788 A010789 A010790 this_sequence A010792 A010793 A010794

nonn

N. J. A. Sloane (njas(AT)research.att.com).