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%I #5 Jul 01 2022 04:13:56
%S 1,1,3,14,88,670,6170,66360,815640,11272800,173132400,2925014400,
%T 53909394000,1076365290000,23144112591600,533193460800000,
%U 13102608591072000,342105146182800000,9457689380931792000,275988880808825184000,8477631163592791200000,273430368958004818560000,9238944655686318693120000
%N Expansion of e.g.f. 1 / (1 - x - x^2/2 - x^3/3 - x^4/4).
%F a(n) = n * a(n-1) + n * (n-1) * a(n-2) / 2 + n * (n-1) * (n-2) * a(n-3) / 3 + n * (n-1) * (n-2) * (n-3) * a(n-4) / 4.
%t nmax = 22; CoefficientList[Series[1/(1 - x - x^2/2 - x^3/3 - x^4/4), {x, 0, nmax}], x] Range[0, nmax]!
%t a[0] = a[1] = 1; a[2] = 3; a[3] = 14; a[n_] := a[n] = n a[n - 1] + n (n - 1) a[n - 2]/2 + n (n - 1) (n - 2) a[n - 3]/3 + n (n - 1) (n - 2) (n - 3) a[n - 4]/4; Table[a[n], {n, 0, 22}]
%Y Cf. A007840, A070945, A080599, A276924, A355293.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Jun 27 2022
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