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%I #18 Jan 14 2023 12:41:12
%S 1,-4,8,-12,15,-16,14,-8,-3,20,-44,76,-117,168,-230,304,-391,492,-608,
%T 740,-889,1056,-1242,1448,-1675,1924,-2196,2492,-2813,3160,-3534,3936,
%U -4367,4828,-5320,5844,-6401,6992,-7618,8280,-8979,9716
%N Expansion of (1 - 2*x^2)/(1 + x)^4. Third column of Riordan triangle A248156.
%C This is the column k=2 sequence of the Riordan triangle A248156 without the leading two zeros.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (-4,-6,-4,-1).
%F O.g.f.: (1 - 2*x^2)/(1 + x)^4 = -1/(1 + x)^4 + 4/(1 + x)^3 -2/(1 + x)^2.
%F a(n) = (-1)^n*(n+1)*(6 + 7*n - n^2)/3!, n >= 0.
%F a(n) = -4*(a(n-1) + a(n-3)) - 6*a(n-2) - a(n-4), n >= 4, with a(0) =1, a(1) = -4, a(2) = 8 and a(3) = -12.
%F a(n)+a(n+1) = A248158(n+1). - _R. J. Mathar_, Mar 13 2021
%p A248159:=n->(-1)^(n+1)*(n+1)*(n^2-7*n-6)/3!: seq(A248159(n),n=0..50); # _Wesley Ivan Hurt_, Oct 07 2014
%t Table[(-1)^(n + 1)*(n + 1)*(n^2 - 7*n - 6)/3!, {n, 0, 50}] (* _Wesley Ivan Hurt_, Oct 07 2014 *)
%o (Magma) [(-1)^(n+1)*(n+1)*(n^2-7*n-6)/Factorial(3) : n in [0..50]]; // _Wesley Ivan Hurt_, Oct 07 2014
%Y Cf. A248156, A248157 (k=0), A248158 (k=1).
%K sign,easy
%O 0,2
%A _Wolfdieter Lang_, Oct 07 2014
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