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
FORMULA
Let a(1) = 1; for n>1, a(n) = Re(Product_{k=1..n} k*exp(i*2*Pi/3)).
EXAMPLE
a(3) = 6 = Re((1*exp(i*2*Pi/3))*(2*exp(i*2*Pi/3))*(3*exp(i*2*Pi/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
KEYWORD
sign,easy
AUTHOR
Gary W. Adamson, Aug 18 2006
EXTENSIONS
More terms from R. J. Mathar, Nov 07 2006
STATUS
approved