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%I #10 Sep 19 2020 02:21:35
%S 1,1,1,-5,-23,-59,601,4831,19825,-302903,-3478319,-19626749,399831961,
%T 5968795405,42864819817,-1091541253529,-20055152560799,
%U -174888464853359,5344185977277985,116600656988485387,1196237099596975561,-42646604098678320299,-1077390070573604975879
%N a(n) = n! * Sum_{k=0..floor(n/3)} (-1)^k / (n-3*k)!.
%H Seiichi Manyama, <a href="/A337750/b337750.txt">Table of n, a(n) for n = 0..449</a>
%F G.f.: Sum_{k>=0} (-1)^k * (3*k)! * x^(3*k) / (1 - x)^(3*k+1).
%F E.g.f.: exp(x) / (1 + x^3).
%F a(0) = a(1) = a(2) = 1; a(n) = 1 - n * (n-1) * (n-2) * a(n-3).
%t Table[n! Sum[(-1)^k/(n - 3 k)!, {k, 0, Floor[n/3]}], {n, 0, 22}]
%t nmax = 22; CoefficientList[Series[Exp[x]/(1 + x^3), {x, 0, nmax}], x] Range[0, nmax]!
%o (PARI) a(n) = n!*sum(k=0, n\3, (-1)^k / (n-3*k)!); \\ _Michel Marcus_, Sep 18 2020
%Y Cf. A182386, A330044, A337749, A337751.
%K sign
%O 0,4
%A _Ilya Gutkovskiy_, Sep 18 2020
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