A343790 Number of ordered partitions of an n-set without blocks of size 7.

1, 1, 3, 13, 75, 541, 4683, 47292, 545819, 7086973, 102242283, 1622530933, 28089498891, 526813752973, 10640325166227, 230258631645913, 5315029292965675, 130353994525735677, 3385061859378821547, 92787606222541942477, 2677254928352340708075, 81110818086045534369661

Offset: 0

Author

Ilya Gutkovskiy, Apr 29 2021

Keywords

• nonn

Crossrefs

Cf. A000670, A032032, A337058, A337059, A343667, A343787, A343788, A343789, A343791, A343792, A343793.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(
      `if`(j=7, 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^7/7! - Exp[x]), {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = If[n == 0, 1, Sum[If[k == 7, 0, Binomial[n, k] a[n - k]], {k, 1, n}]]; Table[a[n], {n, 0, 21}]

Formula

E.g.f.: 1 / (2 + x^7/7! - exp(x)).