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%I #8 Apr 18 2017 16:34:05
%S 1,-3,9,-363,6411,-46569,3615627,-108267435,2044658079,-27994845375,
%T 5887932942123,-90460390681593,475997756735954241,
%U -3681053425472669991,14270353890553782297,-2661381204559253577387,880641541680797362210263
%N Numerators of the exponential expansion of (4/(3*log(1+x)))*(1 - 1/(1+x)^(3/4)).
%C For the denominators see A285060.
%C This gives one third of the numerators of the z-sequence for the Sheffer triangle (exp(3*x), exp(4*x) - 1) shown in A225467. For the notion and use of a- and z- sequences for Sheffer triangles see the W. Lang link under A006232, also for references. The a-sequence of this Sheffer triangle is given by 4*A006232/A006233.
%C For the nontrivial recurrence of {3^n} given by the z-sequence for the m = 0 column of the triangle A225467 see the example for n = 3 below.
%F E.g.f.: (4/(3*log(1+x)))*(1 - 1/(1+x)^(3/4)) for the rational sequence a(n)/A285060(n), n >= 0.
%e The rationals a(n)/A285060(n) start: 1, -3/8, 9/16, -363/256, 6411/1280, -46569/2048, 3615627/28672, -108267435/131072, 2044658079/327680, -27994845375/524288, ...
%e From the z-recurrence for A225467(3, 0) = 3^3 = 27 one finds: 3^3 = 3*3*(1*9 + 40*(-3/8) + 16*(9/16)).
%Y Cf. A006232/A006233 (a-sequence), A284857/A284858 (case [3,1]), A225467.
%K sign,frac,easy
%O 0,2
%A _Wolfdieter Lang_, Apr 13 2017
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