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A161159 a(n) = A003739(n)/(5*A001906(n)*A006238(n)).

%I A161159 #16 Sep 08 2022 08:45:45
%S A161159 9,245,7776,254035,8336079,273725760,8988999201,295197803645,
%T A161159 9694285226784,318360072624475,10454936893196391,343339870595441280,
%U A161159 11275272921720374649,370279686003420394565,12159975800265309667296
%N A161159 a(n) = A003739(n)/(5*A001906(n)*A006238(n)).
%C A161159 Proposed by R. Guy in the seqfan list, Mar 28 2009.
%H A161159 Vincenzo Librandi, <a href="/A161159/b161159.txt">Table of n, a(n) for n = 1..600</a>
%H A161159 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (40,-248,430,-248,40,-1).
%F A161159 a(n) = 40*a(n-1) -248*a(n-2) +430*a(n-3) -248*a(n-4) +40*a(n-5) -a(n-6).
%F A161159 G.f.: x*(9 -115*x +208*x^2 -115*x^3 +9*x^4)/((1-5*x+x^2)*(1-35*x+72*x^2-35*x^3 +x^4)).
%p A161159 seq(coeff(series(x*(9 -115*x +208*x^2 -115*x^3 +9*x^4)/((1-5*x+x^2)*(1-35*x+72*x^2-35*x^3+x^4)), x, n+1), x, n), n = 1..20); # _G. C. Greubel_, Dec 25 2019
%t A161159 CoefficientList[Series[(9-115x+208x^2-115x^3+9x^4)/((1-5x+x^2)*(1-35x+72x^2- 35x^3+x^4)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Dec 19 2012 *)
%o A161159 (Magma) I:=[9,245,7776,254035,8336079,273725760]; [n le 6 select I[n] else 40*Self(n-1)-248*Self(n-2)+430*Self(n-3)-248*Self(n-4)+40*Self(n-5)-Self(n-6): n in [1..16]]; // _Vincenzo Librandi_, Dec 19 2012
%o A161159 (PARI) my(x='x+O('x^30)); Vec(x*(9 -115*x +208*x^2 -115*x^3 +9*x^4)/((1-5*x+ x^2)*(1-35*x+72*x^2-35*x^3+x^4))) \\ _G. C. Greubel_, Dec 25 2019
%o A161159 (Sage)
%o A161159 def A161159_list(prec):
%o A161159     P.<x> = PowerSeriesRing(ZZ, prec)
%o A161159     return P( x*(9 -115*x +208*x^2 -115*x^3 +9*x^4)/((1-5*x+x^2)*(1-35*x+72*x^2-35*x^3+x^4)) ).list()
%o A161159 a=A161159_list(30); a[1:] # _G. C. Greubel_, Dec 25 2019
%K A161159 nonn,easy
%O A161159 1,1
%A A161159 _R. J. Mathar_, Jun 03 2009