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%I #12 Nov 25 2022 06:49:11
%S 1,1,1,-1,-5,-11,-7,31,139,245,-71,-1937,-5989,-6251,25945,144479,
%T 304843,-177899,-3517351,-11743505,-10097381,81902453,433558201,
%U 840235039,-1481279605,-15839941451,-48073840007,-8454966289,564429256219,2518098130645,3490609807769
%N a(n) = Sum_{k=0..floor(n/3)} (-1)^k * (n-k)!/(k! * (n-3*k)!).
%H Seiichi Manyama, <a href="/A358613/b358613.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = (4 * a(n-1) - a(n-2) - 2 * (2*n-3) * a(n-3))/3 for n > 2.
%o (PARI) a(n) = sum(k=0, n\3, (-1)^k*(n-k)!/(k!*(n-3*k)!));
%Y Cf. A247917, A358560.
%K sign
%O 0,5
%A _Seiichi Manyama_, Nov 23 2022
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