%I #17 Aug 05 2024 08:41:53

%S 1,-7,28,-84,210,-462,924,-1714,2975,-4795,6888,-7616,1428,27132,

%T -116276,352632,-919303,2180101,-4815188,10010980,-19650050,36268478,

%U -62075384,95196038,-118778345,73332329,207719344,-1138579904,3670243032,-9852434200,23858720872

%N Expansion of 1/((1 + x)^7 - 2*x^7).

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (-7,-21,-35,-35,-21,-7,1).

%F a(n) = -7*a(n-1) - 21*a(n-2) - 35*a(n-3) - 35*a(n-4) - 21*a(n-5) - 7*a(n-6) + a(n-7).

%F a(n) = (-1)^n * Sum_{k=0..floor(n/7)} (-2)^k * binomial(n+6,7*k+6).

%o (PARI) my(N=40, x='x+O('x^N)); Vec(1/((1+x)^7-2*x^7))

%Y Cf. A108369, A373463.

%Y Cf. A049018.

%K sign,easy

%O 0,2

%A _Seiichi Manyama_, Aug 05 2024