A354063 - OEIS

A354063

Product_{n>=1} 1 / (1 - x^(2*n))^(a(n)/(2*n)!) = cos(x).

-1, 4, 104, 1408, 354944, -21642752, 6204652544, 68669145088, 47215125069824, -78465506362130432, 51085990673656315904, -6994033618612756938752, 15510963121850795776016384, -7220202338641080038690127872, -7469518701197092988127633473536, 11962377309169877924807975108608

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Table of n, a(n) for n=1..16.

FORMULA

E.g.f.: Sum_{k>=1} mu(k) * log(cos(x^k)) / k (even powers only).

MATHEMATICA

nmax = 32; Take[CoefficientList[Series[Sum[MoebiusMu[k] Log[Cos[x^k]]/k, {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!, {1, -1, 2}] // Rest

CROSSREFS

Cf. A170912, A170913, A354055, A354056, A354064, A354065, A354066.

Sequence in context: A006415 A333434 A181396 * A196979 A197164 A356213

Adjacent sequences: A354060 A354061 A354062 * A354064 A354065 A354066

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, May 16 2022

STATUS

approved