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%I #14 Jun 11 2022 03:32:44
%S 1,0,1,1,1,15,11,201,561,4575,25171,187801,1400521,11694735,103903931,
%T 993285801,10113814881,109470594495,1254389104291,15173016742201,
%U 193187969483641,2582736821247855,36172850924874251
%N Boustrophedon transform of ((-2)^n+0^n)/2.
%C Inverse binomial transform of A062272.
%F E.g.f.: (1+exp(-2x))(sec(x)+tan(x))/2.
%F a(n) ~ n! * (1+exp(-Pi)) * (2/Pi)^(n+1). - _Vaclav Kotesovec_, Sep 29 2013
%t 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 *)
%o (Python)
%o from itertools import islice, accumulate
%o def A097953_gen(): # generator of terms
%o blist, m = tuple(), 1
%o while True:
%o yield (blist := tuple(accumulate(reversed(blist),initial=(m+1)//2)))[-1]
%o m *= -2
%o A097953_list = list(islice(A097953_gen(),20)) # _Chai Wah Wu_, Jun 11 2022
%Y Cf. A000734, A062272.
%K nonn
%O 0,6
%A _Paul Barry_, Jan 21 2005
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