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A371605
Expansion of e.g.f. 1 / (1 - x + x^2/2 - x^3/3).
1
1, 1, 1, 2, 10, 50, 230, 1260, 9240, 76440, 651000, 6006000, 62739600, 719518800, 8736327600, 112588476000, 1558917360000, 23070967920000, 360507459312000, 5925688056288000, 102619150714080000, 1869557514945120000, 35676360727207200000
OFFSET
0,4
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] = 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}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 01 2024
STATUS
approved