A343789 Number of ordered partitions of an n-set without blocks of size 6.

1, 1, 3, 13, 75, 541, 4682, 47279, 545611, 7083565, 102182883, 1621425829, 28067555607, 526349480593, 10629883138059, 230009622202373, 5308749619032571, 130186940173803053, 3380385112758108315, 92650130825921846941, 2673020491585091254035, 80974418589343644492805

Offset: 0

Author

Ilya Gutkovskiy, Apr 29 2021

Keywords

• nonn

Crossrefs

Cf. A000670, A032032, A337058, A337059, A343666, A343787, A343788, A343790, A343791, A343792, A343793.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(
      `if`(j=6, 0, a(n-j)*binomial(n, j)), j=1..n))
    end:
seq(a(n), n=0..21);  # Alois P. Heinz, Apr 29 2021

Mathematica

nmax = 21; CoefficientList[Series[1/(2 + x^6/6! - Exp[x]), {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = If[n == 0, 1, Sum[If[k == 6, 0, Binomial[n, k] a[n - k]], {k, 1, n}]]; Table[a[n], {n, 0, 21}]

Formula

E.g.f.: 1 / (2 + x^6/6! - exp(x)).