

A010791


a(n) = n!*(n+2)!/2.


15



1, 3, 24, 360, 8640, 302400, 14515200, 914457600, 73156608000, 7242504192000, 869100503040000, 124281371934720000, 20879270485032960000, 4071457744581427200000, 912006534786239692800000
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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 padic 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. 24882491.
Shaofang Hong, Xingjiang Liu, Squares in (2^21)...(n^21) and padic valuation, arXiv:0810.3366 [math.NT], 20082009.
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: A334775 A153389 A332975 * A145169 A193210 A065761
Adjacent sequences: A010788 A010789 A010790 * A010792 A010793 A010794


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane


STATUS

approved



