A355294 Expansion of e.g.f. 1 / (1 - x - x^2/2 - x^3/3 - x^4/4).

1, 1, 3, 14, 88, 670, 6170, 66360, 815640, 11272800, 173132400, 2925014400, 53909394000, 1076365290000, 23144112591600, 533193460800000, 13102608591072000, 342105146182800000, 9457689380931792000, 275988880808825184000, 8477631163592791200000, 273430368958004818560000, 9238944655686318693120000

Offset: 0

Author

Ilya Gutkovskiy, Jun 27 2022

Keywords

• nonn

Crossrefs

Cf. A007840, A070945, A080599, A276924, A355293.

Programs

Mathematica

nmax = 22; CoefficientList[Series[1/(1 - x - x^2/2 - x^3/3 - x^4/4), {x, 0, nmax}], x] Range[0, nmax]!
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}]

Formula

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.