A216206 a(n) = Product_{i=1..n} ((-2)^i-1).

1, -3, -9, 81, 1215, -40095, -2525985, 325852065, 83092276575, -42626337882975, -43606743654283425, 89350217747626737825, 365889141676531491393375, -2997729737755822508985921375, -49111806293653640164716349886625, 1609344780436736134557590069434814625

Offset: 0

Author

R. J. Mathar, Mar 12 2013

Keywords

• sign
• easy

Comments

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

Crossrefs

Cf. A005329, A015013, A015109, A027871, A062510, A330862.

Programs

Maple

A216206 := proc(n)
        mul( (-2)^i-1, i=1..n) ;
end proc:

Mathematica

Table[(-1)^n QPochhammer[-2, -2, n], {n, 0, 15}] (* Bruno Berselli, Mar 13 2013 *)
Table[Product[(-2)^k-1,{k,n}],{n,0,20}] (* Harvey P. Dale, Oct 21 2024 *)

Formula

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

a(n) = (-3)^n*A015013(n) for n>0, a(0)=1. - Bruno Berselli and Alonso del Arte, Mar 13 2013

a(n) ~ (-1)^(floor(n/2)+1) * c * 2^(n*(n+1)/2), where c = Product_{k>=1} (1 - 1/(-2)^k) = 1.21072413030105918013... (A330862). - Amiram Eldar, Aug 10 2025