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

%I #10 Mar 13 2021 07:45:18

%S 1,-3,4,-4,3,-1,-2,6,-11,17,-24,32,-41,51,-62,74,-87,101,-116,132,

%T -149,167,-186,206,-227,249,-272,296,-321,347,-374,402,-431,461,-492,

%U 524,-557,591,-626,662,-699,737,-776,816,-857,899,-942,986

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

%C This is the column k=1 sequence of the Riordan triangle A248156 without a leading zero.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (-3,-3,-1).

%F O.g.f.: (1 - 2*x^2)/(1 + x)^3 = -2/(1 + x) + 4/(1 + x)^2 - 1/(1 + x)^3.

%F a(n) = (-1)^n*(4*(2*n+1) - (n+1)*(n+2))/2, n >= 0.

%F 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 a(n) = (-1)^(n+1)*A046691(n-5). - _R. J. Mathar_, Mar 13 2021

%F a(n)+a(n+1) = A248157(n+1). - _R. J. Mathar_, Mar 13 2021

%Y Cf. A046691, A148157, A248156(n+1,1).

%K sign,easy

%O 0,2

%A _Wolfdieter Lang_, Oct 05 2014