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A097192 Main diagonal of triangle A097190, in which the n-th row polynomial R_n(y) is formed from the initial (n+1) terms of g.f. A097191(y)^(n+1), where R_n(1/3) = 9^n for all n>=0.

%I A097192 #9 Sep 08 2022 08:45:14
%S A097192 1,24,612,15912,417690,11027016,292215924,7764594552,206732329947,
%T A097192 5512862131920,147193418922264,3934078651195056,105236603919467748,
%U A097192 2817102935690367408,75458114348849127000,2022277464549156603600
%N A097192 Main diagonal of triangle A097190, in which the n-th row polynomial R_n(y) is formed from the initial (n+1) terms of g.f. A097191(y)^(n+1), where R_n(1/3) = 9^n for all n>=0.
%H A097192 G. C. Greubel, <a href="/A097192/b097192.txt">Table of n, a(n) for n = 0..695</a>
%F A097192 G.f.: A(x) = 1/(1-27*x)^(8/9).
%F A097192 a(n) = (n+1)*A097193(n).
%F A097192 Conjecture: n*a(n) +3*(1-9*n)*a(n-1) = 0. - _R. J. Mathar_, Nov 16 2012
%p A097192 seq(coeff(series(1/(1-27*x)^(8/9), x, n+1), x, n), n = 0 ..20); # _G. C. Greubel_, Sep 17 2019
%t A097192 CoefficientList[Series[(1-27*x)^(-8/9), {x,0,20}], x] (* _G. C. Greubel_, Sep 17 2019 *)
%o A097192 (PARI) a(n)=polcoeff(1/(1-27*x+x*O(x^n))^(8/9),n,x)
%o A097192 (Magma) R<x>:=PowerSeriesRing(Rationals(), 20); Coefficients(R!( 1/(1-27*x)^(8/9) )); // _G. C. Greubel_, Sep 17 2019
%o A097192 (Sage)
%o A097192 def A097192_list(prec):
%o A097192     P.<x> = PowerSeriesRing(QQ, prec)
%o A097192     return P(1/(1-27*x)^(8/9)).list()
%o A097192 A097192_list(20) # _G. C. Greubel_, Sep 17 2019
%Y A097192 Cf. A097190, A097191, A097193.
%K A097192 nonn
%O A097192 0,2
%A A097192 _Paul D. Hanna_, Aug 03 2004