A121735 Real term generated from a complex product operation.

1, -1, 6, -12, -60, 720, -2520, -20160, 362880, -1814400, -19958400, 479001600, -3113510400, -43589145600, 1307674368000, -10461394944000, -177843714048000, 6402373705728000, -60822550204416000, -1216451004088320000, 51090942171709440000, -562000363888803840000

Offset

1,3

Comments

The signed sequence is a(n)=n!*T_n(-1/2) for n>1 where T are the Chebyshev polynomials. Therefore a(n)=n!=A000142(n) if 3 divides n, else a(n)=-n!/2=-A001710(n) (n>1). - R. J. Mathar, Aug 25 2006

Links

Table of n, a(n) for n=1..22.

Formula

Let a(1) = (1 Angle 2Pi/3); for n>1, a(n) = Re:[Product(1,n):(n Angle 2Pi/3)].

Example

a(3) = 6 = Re:[(1 Angle 2Pi/3)*(2 Angle 2Pi/3)*(3 Angle 2Pi/3).

Maple

with(orthopoly) ; A121735 := proc(n) if n= 1 then RETURN(1) ; else RETURN( n!*T(n, -1/2)) ; fi ; end: for n from 1 to 25 do print(A121735(n)) ; od ; # R. J. Mathar, Aug 25 2006

Prog

(PARI) A121735(n)={ local(T) ; if(n==1, return(1), x=-1/2 ; T=poltchebi(n) ; return(n!*eval(T)) ; ) ; } { for(n=1, 25, print1(A121735(n), ", ") ; ) ; } \\ R. J. Mathar, Nov 07 2006

Crossrefs

Sequence in context: A123900 A103972 A299855 * A070970 A330974 A045780

Adjacent sequences: A121732 A121733 A121734 * A121736 A121737 A121738

Keyword

sign

Author

Gary W. Adamson, Aug 18 2006

Extensions

More terms from R. J. Mathar, Nov 07 2006

Status

approved