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URL: https://oeis.org/A102590

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A102590
Inverse Boustrophedon transform of 2^n.
1
1, 1, 1, 0, -3, -14, -39, -130, -263, -1214, -179, -21810, 98277, -1021214, 8446881, -82814290, 836117617, -9075846014, 103898533141, -1257148371570, 16004750729757, -213975589371614, 2996827456610601, -43880489398997650, 670443584312526697, -10670445866332254014
OFFSET
0,5
COMMENTS
Binomial transform of (-1)^n*A062162.
LINKS
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
A102590_list = list(islice(A102590_gen(), 20)) # Chai Wah Wu, Jun 10 2022
CROSSREFS
Sequence in context: A027444 A000263 A333293 * A174517 A034130 A117662
KEYWORD
easy,sign
AUTHOR
Paul Barry, Jan 22 2005
STATUS
approved