OFFSET
0,3
COMMENTS
Sum(n>=0,1/a(n))=cos(1)+sin(1).
Sum(n>=0,(Pi/4)^n/a(n))=sqrt(2).
Numerators are in A000012. - Alois P. Heinz, Jan 20 2016
FORMULA
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
E.g.f.: (1 + x)/(1 + x^2). - Ilya Gutkovskiy, Oct 08 2016
MATHEMATICA
Sign@ # Denominator@ # & /@ CoefficientList[Series[Cos@ x + Sin@ x, {x, 0, 20}], x] (* Michael De Vlieger, Oct 08 2016 *)
PROG
(PARI) a(n)=(-1)^(n\2)*n!
CROSSREFS
KEYWORD
frac,sign,easy
AUTHOR
Jaume Oliver Lafont, Sep 09 2009
STATUS
approved