A152143 A sixth degree product form sequence: a(n)=Product[(1 + 4*Sin[k*Pi/n]^2 + 16*Sin[k*Pi/n]^4 + 64*Sin[k*Pi/n]^6), {k, 1, Floor[(n - 1)/2]}].

1, 1, 1, 40, 15, 451, 160, 4901, 1785, 55480, 20295, 630631, 230400, 7152809, 2612233, 81089800, 29614935, 919350379, 335764960, 10423396429, 3806834625, 118178205080, 43161016271, 1339876575119, 489349324800, 15191201606801

Offset

0,4

Links

Table of n, a(n) for n=0..25.

Formula

a(n)=Product[(1 + 4*Sin[k*Pi/n]^2 + 16*Sin[k*Pi/n]^4 + 64*Sin[k*Pi/ n]^6), {k, 1, Floor[(n - 1)/2]}].

Mathematica

f[n_] =Product[(1 + 4*Sin[k*Pi/n]^2 + 16*Sin[k*Pi/n]^4 + 64*Sin[k*Pi/n]^6), {k, 1, Floor[(n - 1)/2]}]; a = Table[f[n], {n, 0, 30}]; Round[a]; FullSimplify[ExpandAll[a]]

Crossrefs

Sequence in context: A126652 A181643 A117831 * A277874 A365051 A033975

Adjacent sequences: A152140 A152141 A152142 * A152144 A152145 A152146

Keyword

nonn

Author

Roger L. Bagula and Gary W. Adamson, Nov 26 2008

Status

approved