A355293 Expansion of e.g.f. 1 / (1 - x - x^2/2 - x^3/3).

1, 1, 3, 14, 82, 610, 5450, 56700, 674520, 9027480, 134236200, 2195701200, 39180094800, 757389032400, 15767305554000, 351689317980000, 8367381470448000, 211518767796336000, 5661504152255952000, 159954273475764768000, 4757034049019572320000, 148547713504322452320000, 4859583724723970642400000

Offset: 0

Author

Ilya Gutkovskiy, Jun 27 2022

Keywords

• nonn

Crossrefs

Cf. A007840, A057693, A080599, A189886, A355294.

Programs

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}]

Formula

a(n) = n * a(n-1) + n * (n-1) * a(n-2) / 2 + n * (n-1) * (n-2) * a(n-3) / 3.