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%I A121735 #13 Sep 15 2024 06:52:19
%S A121735 1,-1,6,-12,-60,720,-2520,-20160,362880,-1814400,-19958400,479001600,
%T A121735 -3113510400,-43589145600,1307674368000,-10461394944000,
%U A121735 -177843714048000,6402373705728000,-60822550204416000,-1216451004088320000,51090942171709440000,-562000363888803840000
%N A121735 Real term generated from a complex product operation.
%C A121735 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
%F A121735 Let a(1) = 1; for n>1, a(n) = Re(Product_{k=1..n} k*exp(i*2*Pi/3)).
%e A121735 a(3) = 6 = Re((1*exp(i*2*Pi/3))*(2*exp(i*2*Pi/3))*(3*exp(i*2*Pi/3))).
%p A121735 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
%o A121735 (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
%K A121735 sign,easy
%O A121735 1,3
%A A121735 _Gary W. Adamson_, Aug 18 2006
%E A121735 More terms from _R. J. Mathar_, Nov 07 2006

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