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A165233
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Signed denominators of terms in series expansion of cos(x)+sin(x).
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0
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1, 1, -2, -6, 24, 120, -720, -5040, 40320, 362880, -3628800, -39916800, 479001600, 6227020800, -87178291200, -1307674368000, 20922789888000, 355687428096000, -6402373705728000, -121645100408832000, 2432902008176640000
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OFFSET
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0,3
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COMMENTS
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Sum(n>=0,1/a(n))=cos(1)+sin(1).
Sum(n>=0,(Pi/4)^n/a(n))=sqrt(2).
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LINKS
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FORMULA
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a(n)=(sin(n*Pi/2)+cos(n*Pi/2))*n!.
a(n)=sqrt(2)*sin((2n+1)*Pi/4)*n!.
a(n)=sqrt(2)*cos((2n-1)*Pi/4)*n!.
G.f. Q(0) where Q(k)= 1 + x*(4*k+1)/(1 + 2*x*(2*k+1)/(1 - 2*x*(2*k+1) - x*(4*k+3)/(1 + x*(4*k+3) - 4*x*(k+1)/(4*x*(k+1) - 1/Q(k+1))))); (continued fraction, 3rd kind, 5-step). - Sergei N. Gladkovskii, Aug 15 2012
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MATHEMATICA
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Sign@ # Denominator@ # & /@ CoefficientList[Series[Cos@ x + Sin@ x, {x, 0, 20}], x] (* Michael De Vlieger, Oct 08 2016 *)
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PROG
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(PARI) a(n)=(-1)^(n\2)*n!
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CROSSREFS
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KEYWORD
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frac,sign,easy
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AUTHOR
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STATUS
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approved
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