OFFSET
0,3
FORMULA
a(n) = n * a(n-1) + n * (n-1) * a(n-2) / 2 + n * (n-1) * (n-2) * a(n-3) / 3.
MATHEMATICA
nmax = 22; CoefficientList[Series[1/(1 - x - x^2/2 - x^3/3), {x, 0, nmax}], x] Range[0, nmax]!
a[0] = a[1] = 1; a[2] = 3; 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}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jun 27 2022
STATUS
approved