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a(n) = product_{i=1..n} ((-2)^i-1).
2

%I #16 Oct 21 2024 10:55:42

%S 1,-3,-9,81,1215,-40095,-2525985,325852065,83092276575,

%T -42626337882975,-43606743654283425,89350217747626737825,

%U 365889141676531491393375,-2997729737755822508985921375,-49111806293653640164716349886625,1609344780436736134557590069434814625

%N a(n) = product_{i=1..n} ((-2)^i-1).

%C Signed partial products of A062510. This implies that all terms from a(1) on are multiples of 3.

%F A015109(n,k) = a(n)/(a(k)*a(n-k)).

%F a(n) = (-3)^n*A015013(n) for n>0, a(0)=1. [_Bruno Berselli_ and _Alonso del Arte_, Mar 13 2013]

%p A216206 := proc(n)

%p mul( (-2)^i-1, i=1..n) ;

%p end proc:

%t Table[(-1)^n QPochhammer[-2, -2, n], {n, 0, 15}] (* _Bruno Berselli_, Mar 13 2013 *)

%t Table[Product[(-2)^k-1,{k,n}],{n,0,20}] (* _Harvey P. Dale_, Oct 21 2024 *)

%Y Cf. A027871, A005329.

%K sign,easy

%O 0,2

%A _R. J. Mathar_, Mar 12 2013