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A141532 Inverse binomial transform of A141425.

%I A141532 #14 Jan 31 2025 07:27:21
%S A141532 1,1,1,-2,4,-8,7,22,-125,376,-878,1756,-3143,5188,-8189,13102,-22928,
%T A141532 45856,-101549,232618,-524285,1137148,-2362874,4725748,-9185771,
%U A141532 17574376,-33554429,64717378,-127043276,254086552,-515347553,1052218462,-2147483645
%N A141532 Inverse binomial transform of A141425.
%C A141532 This is the inverse binomial transform of A141425 if interpreted with offset 0.
%H A141532 G. C. Greubel, <a href="/A141532/b141532.txt">Table of n, a(n) for n = 0..1000</a>
%H A141532 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (-6,-15,-20,-15,-6).
%F A141532 G.f.: (1 +7*x +22*x^2 +39*x^3 +42*x^4 +27*x^5)/((1+x+x^2)*(1+3*x+3*x^2)*(1+2*x)). - _R. J. Mathar_, Nov 11 2008
%F A141532 From _G. C. Greubel_, Mar 30 2021: (Start)
%F A141532 a(n) = (9/2)*[n=0] + (-2)^(n-1) - (3/2)*( ChebyshevU(n, -1/2) + 2*ChebyshevU(n-1, -1/2) + 3^((n-1)/2)*(sqrt(3)*ChebyshevU(n, -sqrt(3)/2) + 2*ChebyshevU(n-1, -sqrt(3)/2)) ).
%F A141532 a(n) = (9/2)*[n=0] + (-2)^(n-1) - (3/2)*(A049347(n) + 2*A049347(n-1) + A000748(n) + 2*A000748(n-1) ). (End)
%t A141532 LinearRecurrence[{-6,-15,-20,-15,-6}, {1,1,1,-2,4,-8}, 40] (* _G. C. Greubel_, Mar 30 2021 *)
%o A141532 (Magma) I:=[1,1,-2,4,-8]; [1] cat [n le 5 select I[n] else -6*Self(n-1) -15*Self(n-2) -20*Self(n-3) -15*Self(n-4) -6*Self(n-5): n in [1..40]]; // _G. C. Greubel_, Mar 30 2021
%o A141532 (Sage)
%o A141532 def A141532_list(prec):
%o A141532     P.<x> = PowerSeriesRing(ZZ, prec)
%o A141532     return P( (1 +7*x +22*x^2 +39*x^3 +42*x^4 +27*x^5)/((1+x+x^2)*(1+3*x+3*x^2)*(1+2*x)) ).list()
%o A141532 A141532_list(40) # _G. C. Greubel_, Mar 30 2021
%Y A141532 Cf. A000748, A049347.
%K A141532 sign
%O A141532 0,4
%A A141532 _Paul Curtz_, Aug 12 2008
%E A141532 Extended by _R. J. Mathar_, Nov 11 2008