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A097185 Row sums of triangle A097181, in which the n-th row polynomial R_n(y) is formed from the initial (n+1) terms of g.f. A097182(y)^(n+1), where R_n(1/2) = 8^n for all n>=0.

%I A097185 #7 Sep 08 2022 08:45:14
%S A097185 1,15,232,3627,57016,899298,14216560,225110307,3568890328,56635884470,
%T A097185 899474459280,14294357356110,227286593929136,3615608476770340,
%U A097185 57538659207907552,915981394162628387,14586262906867731096
%N A097185 Row sums of triangle A097181, in which the n-th row polynomial R_n(y) is formed from the initial (n+1) terms of g.f. A097182(y)^(n+1), where R_n(1/2) = 8^n for all n>=0.
%H A097185 G. C. Greubel, <a href="/A097185/b097185.txt">Table of n, a(n) for n = 0..825</a>
%F A097185 G.f.: A(x) = 2/((1-16*x) + (1-16*x)^(7/8)).
%p A097185 seq(coeff(series(2/((1-16*x) + (1-16*x)^(7/8)), x, n+1), x, n), n = 0 ..30); # _G. C. Greubel_, Sep 17 2019
%t A097185 CoefficientList[Series[2/((1-16*x) +(1-16*x)^(7/8)), {x,0,30}], x] (* _G. C. Greubel_, Sep 17 2019 *)
%o A097185 (PARI) a(n)=polcoeff(2/((1-16*x)+(1-16*x+x*O(x^n))^(7/8)),n,x)
%o A097185 (Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( 2/((1-16*x) + (1-16*x)^(7/8)) )); // _G. C. Greubel_, Sep 17 2019
%o A097185 (Sage)
%o A097185 def A097185_list(prec):
%o A097185     P.<x> = PowerSeriesRing(QQ, prec)
%o A097185     return P(2/((1-16*x) + (1-16*x)^(7/8))).list()
%o A097185 A097185_list(30) # _G. C. Greubel_, Sep 17 2019
%Y A097185 Cf. A097181, A097182.
%K A097185 nonn
%O A097185 0,2
%A A097185 _Paul D. Hanna_, Aug 03 2004