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%I A306941 #16 May 26 2021 00:55:39
%S A306941 1,8,36,120,330,792,1716,3432,6434,11424,19312,31008,46512,62016,
%T A306941 62016,0,-245156,-961376,-2787760,-7065760,-16478280,-36159840,
%U A306941 -75522960,-151045920,-290021896,-534308096,-940325760,-1564496128,-2406819200,-3249142272,-3249142272
%N A306941 Expansion of 1/((1 - x)^8 + x^8).
%H A306941 Seiichi Manyama, <a href="/A306941/b306941.txt">Table of n, a(n) for n = 0..3000</a>
%H A306941 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8,-28,56,-70,56,-28,8,-2).
%F A306941 a(n) = Sum_{k=0..floor(n/8)} (-1)^k*binomial(n+7,8*k+7).
%F A306941 a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - 2*a(n-8) for n > 7.
%t A306941 CoefficientList[Series[1/((1 - x)^8 + x^8), {x, 0, 30}], x] (* _Amiram Eldar_, May 25 2021 *)
%o A306941 (PARI) {a(n) = sum(k=0, n\8, (-1)^k*binomial(n+7, 8*k+7))}
%o A306941 (PARI) N=66; x='x+O('x^N); Vec(1/((1-x)^8+x^8))
%Y A306941 Column 8 of A306914.
%K A306941 sign,easy
%O A306941 0,2
%A A306941 _Seiichi Manyama_, Mar 17 2019

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