A097953 Boustrophedon transform of ((-2)^n+0^n)/2.

1, 0, 1, 1, 1, 15, 11, 201, 561, 4575, 25171, 187801, 1400521, 11694735, 103903931, 993285801, 10113814881, 109470594495, 1254389104291, 15173016742201, 193187969483641, 2582736821247855, 36172850924874251

Offset: 0

Author

Paul Barry, Jan 21 2005

Keywords

• nonn

Comments

Inverse binomial transform of A062272.

Crossrefs

Cf. A000734, A062272.

Programs

Mathematica

CoefficientList[Series[(1+1/E^(2*x))*(1+Sin[x])/Cos[x]/2, {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Sep 29 2013 *)

Python

from itertools import islice, accumulate
def A097953_gen(): # generator of terms
    blist, m = tuple(), 1
    while True:
        yield (blist := tuple(accumulate(reversed(blist),initial=(m+1)//2)))[-1]
        m *= -2
A097953_list = list(islice(A097953_gen(),20)) # Chai Wah Wu, Jun 11 2022

Formula

E.g.f.: (1+exp(-2x))(sec(x)+tan(x))/2.

a(n) ~ n! * (1+exp(-Pi)) * (2/Pi)^(n+1). - Vaclav Kotesovec, Sep 29 2013