cp's OEIS Frontend

A248158 Expansion of (1 - 2*x^2)/(1 + x)^3. Second column of Riordan triangle A248156.

%I A248158 #14 May 30 2025 23:52:44
%S A248158 1,-3,4,-4,3,-1,-2,6,-11,17,-24,32,-41,51,-62,74,-87,101,-116,132,
%T A248158 -149,167,-186,206,-227,249,-272,296,-321,347,-374,402,-431,461,-492,
%U A248158 524,-557,591,-626,662,-699,737,-776,816,-857,899,-942,986
%N A248158 Expansion of (1 - 2*x^2)/(1 + x)^3. Second column of Riordan triangle A248156.
%C A248158 This is the column k=1 sequence of the Riordan triangle A248156 without a leading zero.
%H A248158 G. C. Greubel, <a href="/A248158/b248158.txt">Table of n, a(n) for n = 0..1000</a>
%H A248158 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (-3,-3,-1).
%F A248158 O.g.f.: (1 - 2*x^2)/(1 + x)^3 = -2/(1 + x) + 4/(1 + x)^2 - 1/(1 + x)^3.
%F A248158 a(n) = (-1)^n*(4*(2*n+1) - (n+1)*(n+2))/2, n >= 0.
%F A248158 a(n) = -3*(a(n-1) + a(n-2)) - a(n-3), n >= 3 with a(0) = 1, a(1) = -3 and a(2) = 4.
%F A248158 From _R. J. Mathar_, Mar 13 2021: (Start)
%F A248158 a(n) = (-1)^(n+1)*A046691(n-5).
%F A248158 a(n) + a(n+1) = A248157(n+1). (End)
%F A248158 E.g.f.: (1/2)*(2 - 4*x - x^2)*exp(-x). - _G. C. Greubel_, May 30 2025
%t A248158 Table[(-1)^n*(2+5*n-n^2)/2, {n,0,60}] (* _G. C. Greubel_, May 30 2025 *)
%o A248158 (Magma)
%o A248158 [(-1)^n*(2+5*n-n^2)/2: n in [0..60]]; // _G. C. Greubel_, May 30 2025
%o A248158 (Python)
%o A248158 def A248158(n): return (-1)**n*(2+5*n-n**2)//2
%o A248158 print([A248158(n) for n in range(51)]) # _G. C. Greubel_, May 30 2025
%Y A248158 Cf. A046691, A148157, A248156(n+1,1).
%K A248158 sign,easy
%O A248158 0,2
%A A248158 _Wolfdieter Lang_, Oct 05 2014