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%I #9 Sep 19 2020 02:21:24
%S 1,1,1,1,-23,-119,-359,-839,38641,359857,1809361,6644881,-459055079,
%T -6175146119,-43468088663,-217686301559,20051525850721,
%U 352724346317281,3192296431410721,20250050516224417,-2331591425921837879,-50665325105014242839,-560439561498466178759
%N a(n) = n! * Sum_{k=0..floor(n/4)} (-1)^k / (n-4*k)!.
%H Seiichi Manyama, <a href="/A337751/b337751.txt">Table of n, a(n) for n = 0..450</a>
%F G.f.: Sum_{k>=0} (-1)^k * (4*k)! * x^(4*k) / (1 - x)^(4*k+1).
%F E.g.f.: exp(x) / (1 + x^4).
%F a(0) = a(1) = a(2) = a(3) = 1; a(n) = 1 - n * (n-1) * (n-2) * (n-3) * a(n-4).
%t Table[n! Sum[(-1)^k/(n - 4 k)!, {k, 0, Floor[n/4]}], {n, 0, 22}]
%t nmax = 22; CoefficientList[Series[Exp[x]/(1 + x^4), {x, 0, nmax}], x] Range[0, nmax]!
%o (PARI) a(n) = n!*sum(k=0, n\4, (-1)^k / (n-4*k)!); \\ _Michel Marcus_, Sep 18 2020
%Y Cf. A182386, A330045, A337749, A337750.
%K sign
%O 0,5
%A _Ilya Gutkovskiy_, Sep 18 2020