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%I #19 Apr 04 2024 10:26:55
%S 1,1,1,2,10,50,230,1260,9240,76440,651000,6006000,62739600,719518800,
%T 8736327600,112588476000,1558917360000,23070967920000,360507459312000,
%U 5925688056288000,102619150714080000,1869557514945120000,35676360727207200000
%N Expansion of e.g.f. 1 / (1 - x + x^2/2 - x^3/3).
%F a(n) = n * a(n-1) - n * (n-1) * a(n-2) / 2 + n * (n-1) * (n-2) * a(n-3) / 3.
%t nmax = 22; CoefficientList[Series[1/(1 - x + x^2/2 - x^3/3), {x, 0, nmax}], x] Range[0, nmax]!
%t a[0] = a[1] = a[2] = 1; a[n_] := a[n] = n a[n - 1] - n (n - 1) a[n - 2]/2 + n (n - 1) (n - 2) a[n - 3]/3; Table[a[n], {n, 0, 22}]
%Y Cf. A006252, A009775, A217260, A317111, A355293, A371621.
%K nonn
%O 0,4
%A _Ilya Gutkovskiy_, Apr 01 2024