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%I #10 Dec 08 2021 09:51:01
%S 5,6,6,6,6,-4,-60,-246,-722,-1758,-3754,-7144,-11868,-15646,-9458,
%T 32726,174750,555668,1446564,3310642,6788406,12366066,19107358,
%U 21047904,-1585148,-101419654,-400928730,-1155269658,-2838111242,-6203242964,-12144929980,-20857830310,-29087301442
%N Binomial transform of reflected pentanacci numbers A074062: a(n) = Sum_{k=0..n}(-1)^k*binomial(n, k)*A074062(k).
%H G. C. Greubel, <a href="/A074826/b074826.txt">Table of n, a(n) for n = 0..1000</a>
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,4).
%F a(n) = Sum_{j=0..n} (-1)^j*binomial(n, j)*A074062(j)
%F a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 4*a(n-5), a(0) = 5, a(1) = 6, a(2) = 6, a(3) = 6, a(4) = 6.
%F G.f.: (5 -24*x +45*x^2 -40*x^3 +15*x^4)/(1 -6*x +15*x^2 -20*x^3 +15*x^4 -4*x^5).
%t CoefficientList[Series[(5-24x+45x^2-40x^3+15x^4)/(1-6x+15x^2-20x^3+15x^4-4x^5), {x, 0, 35}], x]
%o (Magma)
%o R<x>:=PowerSeriesRing(Integers(), 40);
%o Coefficients(R!( (5-24*x+45*x^2-40*x^3+15*x^4)/(1-6*x+15*x^2-20*x^3+15*x^4 -4*x^5) )); // _G. C. Greubel_, Jul 08 2021
%o (Sage)
%o def A168823_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o return P( (5-24*x+45*x^2-40*x^3+15*x^4)/(1-6*x+15*x^2-20*x^3+15*x^4-4*x^5) ).list()
%o A168823_list(40) # _G. C. Greubel_, Jul 08 2021
%Y Cf. A074062, A074825.
%K easy,sign
%O 0,1
%A Mario Catalani (mario.catalani(AT)unito.it), Sep 10 2002
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