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A010791 a(n) = n!*(n+2)!/2. 15
1, 3, 24, 360, 8640, 302400, 14515200, 914457600, 73156608000, 7242504192000, 869100503040000, 124281371934720000, 20879270485032960000, 4071457744581427200000, 912006534786239692800000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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

Partial products of positive values of A005563. - Jonathan Vos Post, 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, Oct 21 2008

Equals (-1)^n * (1, 1, 3, 24, 360, ...) dot (1, -4, 9, -16, 25, ...). E.g. a(4) = (1, 1, 3, 24, 360) dot (1, -4, 9, -16, 25) = 1 - 4 + 27 - 384 + 9000 = 8640. - Gary W. Adamson, Apr 21 2009

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Javier Cilleruelo, Squares in (1^2+1)...(n^2+1), Journal of Number Theory 128:8 (2008), pp. 2488-2491.

Shaofang Hong, Xingjiang Liu, Squares in (2^2-1)...(n^2-1) and p-adic valuation, arXiv:0810.3366 [math.NT], 2008-2009.

Index entries for sequences related to factorial numbers

MAPLE

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

MATHEMATICA

Table[n!(n+2)!/2, {n, 0, 20}] (* Vladimir Joseph Stephan Orlovsky, Apr 03 2011 *)

PROG

(MAGMA) [Factorial(n)* Factorial(n+2) / 2: n in [0..20]]; // Vincenzo Librandi, Jun 11 2013

(PARI) a(n) = n!*(n+2)!/2; \\ Michel Marcus, Feb 03 2016

CROSSREFS

Sequence in context: A082166 A144003 A153389 * A145169 A193210 A065761

Adjacent sequences:  A010788 A010789 A010790 * A010792 A010793 A010794

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified April 25 21:06 EDT 2019. Contains 322461 sequences. (Running on oeis4.)