A152122 - OEIS

A152122

a(n) = Product_{k=1..(n-1)/2} 1 + 4*cos(k*Pi/n)^2 + 16*cos(k*Pi/n)^4 + 64*cos(k*Pi/n)^6 + 256*cos(k*Pi/n)^8.

1, 1, 1, 5, 31, 121, 605, 2911, 13361, 64255, 302621, 1428031, 6770555, 31965701, 151200251, 715034375, 3380212751, 15984722176, 75579365455, 357361263031, 1689760311371, 7989708622205, 37778247366211, 178629122366311, 844620446404405, 3993667315453871

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OFFSET

0,4

LINKS

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

FORMULA

a(n) = Product_{k=1..(n-1)/2} Sum_{j=0..4} (2*cos(k*Pi/n))^(2*j).

Empirical g.f.: (1 -15*x^2 -36*x^3 +31*x^4 +130*x^5 -81*x^6 -184*x^7 +265*x^8 -26*x^9 -149*x^10 +60*x^11 +59*x^12 -14*x^13 -15*x^14 -2*x^15 +x^16) / (1 -x -15*x^2 -25*x^3 +45*x^4 +95*x^5 -115*x^6 -105*x^7 +265*x^8 -105*x^9 -115*x^10 +95*x^11 +45*x^12 -25*x^13 -15*x^14 -x^15 +x^16). - Colin Barker, Apr 01 2016

MATHEMATICA

a = Table[Product[1 + 4*Cos[k*Pi/n]^2 + 16*Cos[k*Pi/n]^4 + 64*Cos[k*Pi/n]^6 + 256*Cos[k*Pi/n]^8, {k, 1, (n - 1)/2}], {n, 0, 30}]; Round[%] FullSimplify[ExpandAll[a]]

PROG

(PARI) a(n) = round(prod(k=1, (n-1)/2, 1 + 4*cos(k*Pi/n)^2 + 16*cos(k*Pi/n)^4 + 64*cos(k*Pi/n)^6 + 256*cos(k*Pi/n)^8)) \\ Colin Barker, Apr 01 2016

CROSSREFS

Sequence in context: A212523 A096944 A053699 * A260045 A267938 A041303

Adjacent sequences: A152119 A152120 A152121 * A152123 A152124 A152125

KEYWORD

nonn

AUTHOR

Roger L. Bagula and Gary W. Adamson, Nov 24 2008

EXTENSIONS

Name and formula corrected by Colin Barker, Apr 01 2016

STATUS

approved