A371605 Expansion of e.g.f. 1 / (1 - x + x^2/2 - x^3/3).

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

Links

Table of n, a(n) for n=0..22.

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

Cf. A006252, A009775, A217260, A317111, A355293, A371621.

Sequence in context: A337348 A218778 A320521 * A180266 A355352 A015945

Adjacent sequences: A371602 A371603 A371604 * A371606 A371607 A371608

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 01 2024

Status

approved