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%I #14 Jan 16 2026 09:14:48
%S 1,5,15,35,70,126,210,331,505,770,1221,2080,3822,7385,14501,28201,
%T 53585,99043,178335,314413,546806,946121,1642244,2877925,5107821,
%U 9176831,16634509,30281870,55117511,99979855,180425076,323834920,578593536,1030721985,1834160110,3265884047
%N Expansion of 1 / ((1-x)^5 - x^7).
%H Seiichi Manyama, <a href="/A392546/b392546.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1,0,1).
%F a(n) = Sum_{k=0..floor(n/7)} binomial(n-2*k+4,n-7*k).
%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) + a(n-7).
%o (PARI) my(N=40, x='x+O('x^N)); Vec(1/((1-x)^5-x^7))
%Y Cf. A005709, A049017, A392543, A392544, A392545, A392547.
%Y Cf. A049016, A079675, A368475, A369803, A369804, A390045.
%K nonn,easy
%O 0,2
%A _Seiichi Manyama_, Jan 15 2026