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%I #8 Sep 08 2022 08:45:14
%S 1,1,7,10,58,94,499,868,4360,7951,38407,72508,339997,659380,3019639,
%T 5984968,26880052,54249628,239683171,491235070,2139947788,4444675456,
%U 19125212575,40190140696,171064560433,363227946394,1531088393647
%N Antidiagonal sums of triangle A097186, in which the n-th row polynomial R_n(y) is formed from the initial (n+1) terms of g.f. A057083(y)^(n+1), where R_n(1/3) = 3^n for all n>=0.
%H G. C. Greubel, <a href="/A097187/b097187.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: A(x) = 3*x/((1-9*x^2) + (3*x-1)*(1-9*x^2)^(2/3)).
%F G.f.: A(x) = A004988(x^2)/(1 - x*A097188(x^2)).
%p seq(coeff(series(3*x/((1-9*x^2) +(3*x-1)*(1-9*x^2)^(2/3)), x, n+2), x, n), n = 0..30); # _G. C. Greubel_, Sep 17 2019
%t CoefficientList[Series[3*x/((1-9*x^2) +(3*x-1)*(1-9*x^2)^(2/3)), {x, 0, 30}], x] (* _G. C. Greubel_, Sep 17 2019 *)
%o (PARI) a(n)=polcoeff(3*x/((1-9*x^2)+(3*x-1)*(1-9*x^2+x^2*O(x^n))^(2/3)), n,x)
%o (Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( 3*x/((1-9*x^2) + (3*x-1)*(1-9*x^2)^(2/3)) )); // _G. C. Greubel_, Sep 17 2019
%o (Sage)
%o def A097187_list(prec):
%o P.<x> = PowerSeriesRing(QQ, prec)
%o return P(3*x/((1-9*x^2) + (3*x-1)*(1-9*x^2)^(2/3))).list()
%o A097187_list(30) # _G. C. Greubel_, Sep 17 2019
%Y Cf. A004988, A057083, A097186, A097188.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Aug 03 2004
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