OFFSET
0,5
COMMENTS
Binomial transform of (-1)^n*A062162.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..200
FORMULA
E.g.f.: exp(2x)/(sec(x)+tan(x)) = cos(x)exp(2x)/(1+sin(x)).
a(n) ~ (-1)^n * n^(n+1/2)*2^(n+5/2)/(Pi^(n+1/2)*exp(n+Pi)). - Vaclav Kotesovec, Sep 29 2013
G.f.: E(0)*x/(x-1)/(1-2*x) + 1/(1-2*x), where E(k) = 1 - x^2*(k+1)*(k+2)/( x^2*(k+1)*(k+2) - 2*(x*(k-1)+1)*(x*k+1)/E(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Jan 16 2014
MAPLE
a:= n-> n!*coeff(series(exp(2*x)/(sec(x)+tan(x)), x, n+1), x, n):
seq(a(n), n=0..30); # Alois P. Heinz, Sep 29 2013
MATHEMATICA
CoefficientList[Series[Cos[x]*E^(2*x)/(1+Sin[x]), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Sep 29 2013 *)
PROG
(Python)
from itertools import islice, accumulate
from operator import sub
def A102590_gen(): # generator of terms
blist, m = tuple(), 1
while True:
yield (blist := tuple(accumulate(reversed(blist), func=sub, initial=m)))[-1]
m *= 2
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Paul Barry, Jan 22 2005
STATUS
approved