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A097183 Main diagonal 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 A097183 #14 Sep 08 2022 08:45:14
%S A097183 1,14,210,3220,49910,778596,12198004,191682920,3019005990,47633205620,
%T A097183 752604648796,11904837171864,188493255221180,2986893121197160,
%U A097183 47363590921840680,751502309293205456,11930099160029636614
%N A097183 Main diagonal 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 A097183 Vincenzo Librandi, <a href="/A097183/b097183.txt">Table of n, a(n) for n = 0..200</a>
%F A097183 G.f.: A(x) = 1/(1-16*x)^(7/8).
%F A097183 a(n) = (n+1)*A097184(n).
%F A097183 a(n) = (n+1) * 16^n * Gamma(n+7/8) / (Gamma(7/8) * Gamma(n+2)). - _Vaclav Kotesovec_, Feb 09 2014
%p A097183 seq(coeff(series((1-16*x)^(-7/8), x, n+1), x, n), n = 0 ..20); # _G. C. Greubel_, Sep 17 2019
%t A097183 Table[FullSimplify[(n+1)*16^n*Gamma[n+7/8]/(Gamma[7/8]*Gamma[n+2])], {n, 0, 20}] (* _Vaclav Kotesovec_, Feb 09 2014 *)
%t A097183 CoefficientList[Series[(1-16*x)^(-7/8), {x,0,20}], x] (* _G. C. Greubel_, Sep 17 2019 *)
%o A097183 (PARI) a(n)=polcoeff(1/(1-16*x+x*O(x^n))^(7/8),n,x)
%o A097183 (Magma) R<x>:=PowerSeriesRing(Rationals(), 20); Coefficients(R!( (1-16*x)^(-7/8) )); // _G. C. Greubel_, Sep 17 2019
%o A097183 (Sage)
%o A097183 def A097183_list(prec):
%o A097183     P.<x> = PowerSeriesRing(QQ, prec)
%o A097183     return P((1-16*x)^(-7/8)).list()
%o A097183 A097183_list(20) # _G. C. Greubel_, Sep 17 2019
%Y A097183 Cf. A097181, A097182, A097184.
%K A097183 nonn
%O A097183 0,2
%A A097183 _Paul D. Hanna_, Aug 03 2004